diff --git a/cryptarchia/cryptarchia.py b/cryptarchia/cryptarchia.py
index a8e3ac0..6f2f310 100644
--- a/cryptarchia/cryptarchia.py
+++ b/cryptarchia/cryptarchia.py
@@ -10,7 +10,6 @@ from collections import defaultdict
 
 import numpy as np
 
-
 logger = logging.getLogger(__name__)
 
 
@@ -368,16 +367,15 @@ class EpochState:
 class Follower:
     def __init__(self, genesis_state: LedgerState, config: Config):
         self.config = config
-        self.forks = []
+        self.forks: list[Id] = []
         self.local_chain = genesis_state.block.id()
         self.genesis_state = genesis_state
         self.ledger_state = {genesis_state.block.id(): genesis_state.copy()}
         self.epoch_state = {}
 
-    def validate_header(self, block: BlockHeader) -> bool:
+    def validate_header(self, block: BlockHeader):
         # TODO: verify blocks are not in the 'future'
         if block.parent not in self.ledger_state:
-            logger.warning("We have not seen block parent")
             raise ParentNotFound
 
         current_state = self.ledger_state[block.parent].copy()
@@ -397,8 +395,7 @@ class Follower:
             # We take a shortcut for (1.) by restricting orphans to proofs we've
             # already processed in other branches.
             if orphan.id() not in self.ledger_state:
-                logger.warning("missing orphan proof")
-                return False
+                raise MissingOrphanProof
 
             # (2.) is satisfied by verifying the proof against current state ensuring:
             # - it is a valid proof
@@ -410,21 +407,21 @@ class Follower:
                 epoch_state,
                 current_state,
             ):
-                logger.warning("invalid orphan proof")
-                return False
+                raise InvalidOrphanProof
 
             # if an adopted leadership proof is valid we need to apply its
             # effects to the ledger state
             current_state.apply_leader_proof(orphan.leader_proof)
 
         # TODO: this is not the full block validation spec, only slot leader is verified
-        return self.verify_slot_leader(
+        if not self.verify_slot_leader(
             block.slot,
             block.parent,
             block.leader_proof,
             epoch_state,
             current_state,
-        )
+        ):
+            raise InvalidLeaderProof
 
     def verify_slot_leader(
         self,
@@ -452,9 +449,7 @@ class Follower:
             logger.warning("dropping already processed block")
             return False
 
-        if not self.validate_header(block):
-            logger.warning("invalid header")
-            return False
+        self.validate_header(block)
 
         new_state = self.ledger_state[block.parent].copy()
         new_state.apply(block)
@@ -803,7 +798,23 @@ def maxvalid_bg(
 
 
 class ParentNotFound(Exception):
-    pass
+    def __str__(self):
+        return "Parent not found"
+
+
+class MissingOrphanProof(Exception):
+    def __str__(self):
+        return "Missing orphan proof"
+
+
+class InvalidOrphanProof(Exception):
+    def __str__(self):
+        return "Invalid orphan proof"
+
+
+class InvalidLeaderProof(Exception):
+    def __str__(self):
+        return "Invalid leader proof"
 
 
 if __name__ == "__main__":
diff --git a/cryptarchia/sync.py b/cryptarchia/sync.py
index 30ebcd6..6921c3b 100644
--- a/cryptarchia/sync.py
+++ b/cryptarchia/sync.py
@@ -18,110 +18,164 @@ def sync(local: Follower, peers: list[Follower]):
 
     # Repeat the sync process until no peer has a tip ahead of the local tip,
     # because peers' tips may advance during the sync process.
+    block_fetcher = BlockFetcher(peers)
+    rejected_blocks: set[Id] = set()
     while True:
         # Fetch blocks from the peers in the range of slots from the local tip to the latest tip.
         # Gather orphaned blocks, which are blocks from forks that are absent in the local block tree.
+
         start_slot = local.tip().slot
         orphans: set[BlockHeader] = set()
-        # Filter peers that have a tip ahead of the local tip
-        # and group peers by their tip to minimize the number of fetches.
-        groups = filter_and_group_peers_by_tip(peers, start_slot)
-        # Finish the sync process if no peer has a tip ahead of the local tip.
-        if len(groups) == 0:
-            return
+        num_blocks = 0
+        for block in block_fetcher.fetch_blocks_from(start_slot):
+            num_blocks += 1
+            # Reject blocks that have been rejected in the past
+            # or whose parent has been rejected.
+            if {block.id(), block.parent} & rejected_blocks:
+                rejected_blocks.add(block.id())
+                continue
 
-        for group in groups.values():
-            for block in fetch_blocks_by_slot(group, start_slot):
-                try:
-                    local.on_block(block)
-                    orphans.discard(block)
-                except ParentNotFound:
-                    orphans.add(block)
+            try:
+                local.on_block(block)
+                orphans.discard(block)
+            except ParentNotFound:
+                orphans.add(block)
+            except Exception:
+                rejected_blocks.add(block.id())
+
+        # Finish the sync process if no block has been fetched,
+        # which means that no peer has a tip ahead of the local tip.
+        if num_blocks == 0:
+            return
 
         # Backfill the orphan forks starting from the orphan blocks with applying fork choice rule.
         #
         # Sort the orphan blocks by slot in descending order to minimize the number of backfillings.
         for orphan in sorted(orphans, key=lambda b: b.slot, reverse=True):
-            # Skip the orphan block if it has been processed during the previous backfillings.
-            # (i.e. if it has been already added to the local block tree)
-            if orphan not in local.ledger_state:
-                backfill_fork(local, peers, orphan)
+            # Skip the orphan block if it has been processed during the previous backfillings
+            # (i.e. if it has been already added to the local block tree).
+            # Or, skip if it has been rejected during the previous backfillings.
+            if (
+                orphan.id() not in local.ledger_state
+                and orphan.id() not in rejected_blocks
+            ):
+                try:
+                    backfill_fork(local, orphan, block_fetcher)
+                except InvalidBlockFromBackfillFork as e:
+                    rejected_blocks.update(block.id() for block in e.invalid_suffix)
 
 
-def filter_and_group_peers_by_tip(
-    peers: list[Follower], start_slot: Slot
-) -> dict[BlockHeader, list[Follower]]:
-    # Group peers by their tip.
-    # Filter only the peers whose tip is ahead of the start_slot.
-    groups: dict[BlockHeader, list[Follower]] = defaultdict(list)
-    for peer in peers:
-        if peer.tip().slot.absolute_slot > start_slot.absolute_slot:
-            groups[peer.tip()].append(peer)
-    return groups
-
-
-def fetch_blocks_by_slot(
-    peers: list[Follower], start_slot: Slot
-) -> Generator[BlockHeader, None, None]:
-    # Fetch blocks in the given range of slots from one of the peers.
-    # Blocks should be returned in order of slot.
-    # If a peer fails, try the next peer.
-    for peer in peers:
-        try:
-            for block in peer.blocks_by_slot(start_slot):
-                yield block
-                # Update start_slot for the potential try with the next peer.
-                start_slot = block.slot
-            # The peer successfully returned all blocks. No need to try the next peer.
-            break
-        except Exception:
-            continue
-
-
-def backfill_fork(local: Follower, peers: list[Follower], fork_tip: BlockHeader):
+def backfill_fork(
+    local: Follower,
+    fork_tip: BlockHeader,
+    block_fetcher: "BlockFetcher",
+):
     # Backfills a fork, which is absent in the local block tree, by fetching blocks from the peers.
     # During backfilling, the fork choice rule is continuously applied.
     #
     # If necessary, the local honest chain is also backfilled for the fork choice rule.
-    # This can happen if the honest chain has been built not from the genesis
-    # (e.g. checkpoint sync, or a partially backfilled chain).
+    # This can happen if the honest chain has been built not from the genesis (i.e. checkpoint sync).
 
     _, tip_suffix, _, fork_suffix = common_prefix_depth_from_chains(
-        fetch_chain_blocks(local.tip_id(), local, peers),
-        fetch_chain_blocks(fork_tip.id(), local, peers),
+        block_fetcher.fetch_chain_backward(local.tip_id(), local),
+        block_fetcher.fetch_chain_backward(fork_tip.id(), local),
     )
 
     # First, backfill the local honest chain if some blocks are missing.
-    # Just applying the blocks to the ledger state is enough,
-    # instead of calling `on_block` which updates the tip (by fork choice).
-    # because we're just backfilling the old part of the current tip.
+    # In other words, backfill the local block tree, which contains the honest chain.
     for block in tip_suffix:
-        local.apply_block_to_ledger_state(block)
+        try:
+            # Just apply the block to the ledger state is enough
+            # instead of calling `on_block` which runs the fork choice rule.
+            local.apply_block_to_ledger_state(block)
+        except Exception as e:
+            raise InvalidBlockTree(e)
 
-    # Then, process blocks in the fork suffix by applying fork choice rule.
-    for block in fork_suffix:
-        local.on_block(block)
+    # Then, add blocks in the fork suffix with applying fork choice rule.
+    # After all, add the tip of the fork suffix to apply the fork choice rule.
+    for i, block in enumerate(fork_suffix):
+        try:
+            local.on_block(block)
+        except Exception as e:
+            raise InvalidBlockFromBackfillFork(e, fork_suffix[i:])
 
 
-def fetch_chain_blocks(
-    tip: Id, local: Follower, peers: list[Follower]
-) -> Generator[BlockHeader, None, None]:
-    # Fetches a chain of blocks from the peers, starting from the given tip to the genesis.
-    # Attempts to extend the chain as much as possible by querying multiple peers,
-    # considering that not all peers may have the full chain (from the genesis).
+class BlockFetcher:
+    # NOTE: This class is a mock, which uses a naive approach to fetch blocks from multiple peers.
+    # In real implementation, any optimized way can be used, such as parallel fetching.
 
-    id = tip
-    # First, try to iterate the chain from the local block tree.
-    for block in iter_chain_blocks(id, local.ledger_state):
-        yield block
-        if block.id() == local.genesis_state.block.id():
-            return
-        id = block.parent
+    def __init__(self, peers: list[Follower]):
+        self.peers = peers
 
-    # Try to continue by fetching the remaining blocks from the peers
-    for peer in peers:
-        for block in iter_chain_blocks(id, peer.ledger_state):
+    def fetch_blocks_from(self, start_slot: Slot) -> Generator[BlockHeader, None, None]:
+        # Filter peers that have a tip ahead of the local tip
+        # and group peers by their tip to minimize the number of fetches.
+        groups = self.filter_and_group_peers_by_tip(start_slot)
+        for group in groups.values():
+            for block in BlockFetcher.fetch_blocks_by_slot(group, start_slot):
+                yield block
+
+    def filter_and_group_peers_by_tip(
+        self, start_slot: Slot
+    ) -> dict[BlockHeader, list[Follower]]:
+        # Group peers by their tip.
+        # Filter only the peers whose tip is ahead of the start_slot.
+        groups: dict[BlockHeader, list[Follower]] = defaultdict(list)
+        for peer in self.peers:
+            if peer.tip().slot.absolute_slot > start_slot.absolute_slot:
+                groups[peer.tip()].append(peer)
+        return groups
+
+    @staticmethod
+    def fetch_blocks_by_slot(
+        peers: list[Follower], start_slot: Slot
+    ) -> Generator[BlockHeader, None, None]:
+        # Fetch blocks in the given range of slots from one of the peers.
+        # Blocks should be returned in order of slot.
+        # If a peer fails, try the next peer.
+        for peer in peers:
+            try:
+                for block in peer.blocks_by_slot(start_slot):
+                    yield block
+                    # Update start_slot for the potential try with the next peer.
+                    start_slot = block.slot
+                # The peer successfully returned all blocks. No need to try the next peer.
+                break
+            except Exception:
+                continue
+
+    def fetch_chain_backward(
+        self, tip: Id, local: Follower
+    ) -> Generator[BlockHeader, None, None]:
+        # Fetches a chain of blocks from the peers, starting from the given tip to the genesis.
+        # Attempts to extend the chain as much as possible by querying multiple peers,
+        # considering that not all peers may have the full chain (from the genesis).
+
+        id = tip
+        # First, try to iterate the chain from the local block tree.
+        for block in iter_chain_blocks(id, local.ledger_state):
             yield block
             if block.id() == local.genesis_state.block.id():
                 return
             id = block.parent
+
+        # Try to continue by fetching the remaining blocks from the peers
+        for peer in self.peers:
+            for block in iter_chain_blocks(id, peer.ledger_state):
+                yield block
+                if block.id() == local.genesis_state.block.id():
+                    return
+                id = block.parent
+
+
+class InvalidBlockTree(Exception):
+    def __init__(self, cause: Exception):
+        super().__init__()
+        self.cause = cause
+
+
+class InvalidBlockFromBackfillFork(Exception):
+    def __init__(self, cause: Exception, invalid_suffix: list[BlockHeader]):
+        super().__init__()
+        self.cause = cause
+        self.invalid_suffix = invalid_suffix
diff --git a/cryptarchia/test_ledger_state_update.py b/cryptarchia/test_ledger_state_update.py
index 32425e5..d66abf0 100644
--- a/cryptarchia/test_ledger_state_update.py
+++ b/cryptarchia/test_ledger_state_update.py
@@ -1,10 +1,14 @@
 from unittest import TestCase
 
-import numpy as np
-
-from .cryptarchia import Follower, Coin, ParentNotFound, iter_chain
-
-from .test_common import mk_config, mk_block, mk_genesis_state
+from .cryptarchia import (
+    Coin,
+    Follower,
+    InvalidLeaderProof,
+    MissingOrphanProof,
+    ParentNotFound,
+    iter_chain,
+)
+from .test_common import mk_block, mk_config, mk_genesis_state
 
 
 class TestLedgerStateUpdate(TestCase):
@@ -46,7 +50,8 @@ class TestLedgerStateUpdate(TestCase):
         assert follower.tip_state().verify_unspent(leader_coin.nullifier()) == False
 
         reuse_coin_block = mk_block(slot=1, parent=block, coin=leader_coin)
-        follower.on_block(reuse_coin_block)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(reuse_coin_block)
 
         # Follower should *not* have accepted the block
         assert len(list(iter_chain(follower.tip_id(), follower.ledger_state))) == 2
@@ -170,7 +175,8 @@ class TestLedgerStateUpdate(TestCase):
         # so that the new block can be accepted only if that is the snapshot used
         # first, verify that if we don't change the state, the block is not accepted
         block_4 = mk_block(slot=40, parent=block_3, coin=Coin(sk=4, value=100))
-        follower.on_block(block_4)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_4)
         assert follower.tip() == block_3
         # then we add the coin to "spendable commitments" associated with slot 9
         follower.ledger_state[block_2.id()].commitments_spend.add(
@@ -194,7 +200,8 @@ class TestLedgerStateUpdate(TestCase):
 
         # coin can't be reused to win following slots:
         block_2_reuse = mk_block(slot=1, parent=block_1, coin=coin)
-        follower.on_block(block_2_reuse)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_2_reuse)
         assert follower.tip() == block_1
 
         # but the evolved coin is eligible
@@ -225,7 +232,8 @@ class TestLedgerStateUpdate(TestCase):
 
         # the new coin is not yet eligible for elections
         block_0_1_attempt = mk_block(slot=1, parent=block_0_0, coin=coin_new)
-        follower.on_block(block_0_1_attempt)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_0_1_attempt)
         assert follower.tip() == block_0_0
 
         # whereas the evolved coin from genesis can be spent immediately
@@ -239,7 +247,8 @@ class TestLedgerStateUpdate(TestCase):
         # stake distribution snapshot is taken at the beginning of the previous epoch
 
         block_1_0 = mk_block(slot=20, parent=block_0_1, coin=coin_new)
-        follower.on_block(block_1_0)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_1_0)
         assert follower.tip() == block_0_1
 
         # ---- EPOCH 2 ----
@@ -268,7 +277,8 @@ class TestLedgerStateUpdate(TestCase):
         coin_new = coin.evolve()
         coin_new_new = coin_new.evolve()
         block_0_1 = mk_block(slot=1, parent=block_0_0, coin=coin_new_new)
-        follower.on_block(block_0_1)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_0_1)
         # the coin evolved twice should not be accepted as it is not in the lead commitments
         assert follower.tip() == block_0_0
 
@@ -284,7 +294,8 @@ class TestLedgerStateUpdate(TestCase):
             coin=coin_orphan.evolve(),
             orphaned_proofs=[orphan],
         )
-        follower.on_block(block_0_1)
+        with self.assertRaises(MissingOrphanProof):
+            follower.on_block(block_0_1)
 
         # since follower had not seen this orphan prior to being included as
         # an orphan proof, it will be rejected
diff --git a/cryptarchia/test_sync.py b/cryptarchia/test_sync.py
index b0ce4ad..101e8e0 100644
--- a/cryptarchia/test_sync.py
+++ b/cryptarchia/test_sync.py
@@ -1,12 +1,13 @@
 from unittest import TestCase
 
-from cryptarchia.cryptarchia import Coin, Follower
-from cryptarchia.sync import sync
+from cryptarchia.cryptarchia import BlockHeader, Coin, Follower
+from cryptarchia.sync import InvalidBlockTree, sync
 from cryptarchia.test_common import mk_block, mk_config, mk_genesis_state
 
 
 class TestSync(TestCase):
     def test_sync_single_chain_from_genesis(self):
+        # Prepare a peer with a single chain:
         # b0 - b1 - b2 - b3
         coin = Coin(sk=0, value=10)
         config = mk_config([coin])
@@ -21,12 +22,15 @@ class TestSync(TestCase):
         self.assertEqual(peer.tip(), b3)
         self.assertEqual(peer.forks, [])
 
+        # Start a sync from genesis.
+        # Result: The same block tree as the peer's.
         local = Follower(genesis, config)
         sync(local, [peer])
         self.assertEqual(local.tip(), peer.tip())
         self.assertEqual(local.forks, peer.forks)
 
     def test_sync_single_chain_from_middle(self):
+        # Prepare a peer with a single chain:
         # b0 - b1 - b2 - b3
         coin = Coin(sk=0, value=10)
         config = mk_config([coin])
@@ -41,16 +45,19 @@ class TestSync(TestCase):
         self.assertEqual(peer.tip(), b3)
         self.assertEqual(peer.forks, [])
 
+        # Start a sync from a tree:
+        # b0 - b1
+        #
+        # Result: The same block tree as the peer's.
         local = Follower(genesis, config)
-        # add until b1
         for b in [b0, b1]:
             peer.on_block(b)
-        # start syncing from b1
         sync(local, [peer])
         self.assertEqual(local.tip(), peer.tip())
         self.assertEqual(local.forks, peer.forks)
 
     def test_sync_forks_from_genesis(self):
+        # Prepare a peer with forks:
         # b0 - b1 - b2 - b5 == tip
         #    \
         #      b3 - b4
@@ -69,12 +76,15 @@ class TestSync(TestCase):
         self.assertEqual(peer.tip(), b5)
         self.assertEqual(peer.forks, [b4.id()])
 
+        # Start a sync from genesis.
+        # Result: The same block tree as the peer's.
         local = Follower(genesis, config)
         sync(local, [peer])
         self.assertEqual(local.tip(), peer.tip())
         self.assertEqual(local.forks, peer.forks)
 
     def test_sync_forks_from_middle(self):
+        # Prepare a peer with forks:
         # b0 - b1 - b2 - b5 == tip
         #    \
         #      b3 - b4
@@ -93,9 +103,12 @@ class TestSync(TestCase):
         self.assertEqual(peer.tip(), b5)
         self.assertEqual(peer.forks, [b4.id()])
 
+        # Start a sync from a tree:
         # b0 - b1
         #    \
         #      b3
+        #
+        # Result: The same block tree as the peer's.
         local = Follower(genesis, config)
         for b in [b0, b1, b3]:
             peer.on_block(b)
@@ -104,6 +117,7 @@ class TestSync(TestCase):
         self.assertEqual(local.forks, peer.forks)
 
     def test_sync_forks_by_backfilling(self):
+        # Prepare a peer with forks:
         # b0 - b1 - b2 - b5 == tip
         #    \
         #      b3 - b4
@@ -123,7 +137,10 @@ class TestSync(TestCase):
         self.assertEqual(peer.forks, [b4.id()])
         self.assertEqual(len(peer.ledger_state), 7)
 
+        # Start a sync from a tree without the fork:
         # b0 - b1
+        #
+        # Result: The same block tree as the peer's.
         local = Follower(genesis, config)
         for b in [b0, b1]:
             peer.on_block(b)
@@ -133,6 +150,7 @@ class TestSync(TestCase):
         self.assertEqual(len(local.ledger_state), len(peer.ledger_state))
 
     def test_sync_multiple_peers_from_genesis(self):
+        # Prepare multiple peers:
         # Peer-0:                b5
         #                      /
         # Peer-1: b0 - b1 - b2
@@ -163,15 +181,109 @@ class TestSync(TestCase):
         self.assertEqual(peer2.tip(), b4)
         self.assertEqual(peer2.forks, [])
 
+        # Start a sync from genesis.
+        #
+        # Result: A merged block tree
+        #                b5
+        #              /
+        # b0 - b1 - b2
+        #    \
+        #      b3 - b4
         local = Follower(genesis, config)
         sync(local, [peer0, peer1, peer2])
         self.assertEqual(local.tip(), b5)
         self.assertEqual(local.forks, [b4.id()])
         self.assertEqual(len(local.ledger_state), 7)
 
+    def test_reject_invalid_blocks(self):
+        # Prepare a peer with invalid blocks:
+        # b0 - b1 - b2 - b3 - (invalid_b4) - (invalid_b5)
+        #
+        # First, build a valid chain (b0 ~ b3):
+        coin = Coin(sk=0, value=10)
+        config = mk_config([coin])
+        genesis = mk_genesis_state([coin])
+        peer = Follower(genesis, config)
+        b0, coin = mk_block(genesis.block, 1, coin), coin.evolve()
+        b1, coin = mk_block(b0, 2, coin), coin.evolve()
+        b2, coin = mk_block(b1, 3, coin), coin.evolve()
+        b3, coin = mk_block(b2, 4, coin), coin.evolve()
+        for b in [b0, b1, b2, b3]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b3)
+        self.assertEqual(peer.forks, [])
+
+        # And deliberately, add invalid blocks (b4 ~ b5):
+        fake_coin = Coin(sk=1, value=10)
+        b4, fake_coin = mk_block(b3, 5, fake_coin), fake_coin.evolve()
+        b5, fake_coin = mk_block(b4, 6, fake_coin), fake_coin.evolve()
+        apply_invalid_block_to_ledger_state(peer, b4)
+        apply_invalid_block_to_ledger_state(peer, b5)
+        # the tip shouldn't be changed.
+        self.assertEqual(peer.tip(), b3)
+        self.assertEqual(peer.forks, [])
+
+        # Start a sync from genesis.
+        #
+        # Result: The same honest chain, but without invalid blocks.
+        # b0 - b1 - b2 - b3 == tip
+        local = Follower(genesis, config)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+
+    def test_reject_invalid_blocks_from_backfilling(self):
+        # Prepare a peer with invalid blocks in a fork:
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2 - (invalid_b6) - (invalid_b7)
+        #
+        # First, build a valid chain (b0 ~ b5):
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b3, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b4, c_a = mk_block(b3, 4, c_a), c_a.evolve()
+        b5, c_a = mk_block(b4, 5, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # And deliberately, add invalid blocks (b6 ~ b7):
+        fake_coin = Coin(sk=2, value=10)
+        b6, fake_coin = mk_block(b2, 3, fake_coin), fake_coin.evolve()
+        b7, fake_coin = mk_block(b6, 4, fake_coin), fake_coin.evolve()
+        apply_invalid_block_to_ledger_state(peer, b6)
+        apply_invalid_block_to_ledger_state(peer, b7)
+        # the tip shouldn't be changed.
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # Start a sync from a tree:
+        # b0 - b1 - b3 - b4
+        #
+        # Result: The same forks, but without invalid blocks
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2
+        local = Follower(genesis, config)
+        for b in [b0, b1, b3, b4]:
+            peer.on_block(b)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+        self.assertNotIn(b6.id(), local.ledger_state)
+        self.assertNotIn(b7.id(), local.ledger_state)
+
 
 class TestSyncFromCheckpoint(TestCase):
     def test_sync_single_chain(self):
+        # Prepare a peer with a single chain:
         # b0 - b1 - b2 - b3
         #           ||
         #       checkpoint
@@ -188,18 +300,17 @@ class TestSyncFromCheckpoint(TestCase):
         self.assertEqual(peer.tip(), b3)
         self.assertEqual(peer.forks, [])
 
-        # Start from the checkpoint:
+        # Start a sync from the checkpoint:
         # () - () - b2
         #           ||
         #       checkpoint
+        #
+        # Result: A honest chain without historical blocks
+        # () - () - b2 - b3
         checkpoint = peer.ledger_state[b2.id()]
         local = Follower(genesis, config)
         local.apply_checkpoint(checkpoint)
         sync(local, [peer])
-        # Result:
-        # () - () - b2 - b3
-        #           ||
-        #       checkpoint
         self.assertEqual(local.tip(), peer.tip())
         self.assertEqual(local.forks, peer.forks)
         self.assertEqual(
@@ -207,6 +318,7 @@ class TestSyncFromCheckpoint(TestCase):
         )
 
     def test_sync_forks(self):
+        # Prepare a peer with forks:
         #       checkpoint
         #           ||
         # b0 - b1 - b2 - b5 == tip
@@ -227,23 +339,25 @@ class TestSyncFromCheckpoint(TestCase):
         self.assertEqual(peer.tip(), b5)
         self.assertEqual(peer.forks, [b4.id()])
 
-        # Start from the checkpoint:
+        # Start a sync from the checkpoint:
         #       checkpoint
         #           ||
         # () - () - b2
+        #
+        # Result: Backfilled forks.
+        # b0 - b1 - b2 - b5 == tip
+        #    \
+        #      b3 - b4
         checkpoint = peer.ledger_state[b2.id()]
         local = Follower(genesis, config)
         local.apply_checkpoint(checkpoint)
         sync(local, [peer])
-        # Result:
-        # b0 - b1 - b2 - b5 == tip
-        #    \
-        #      b3 - b4
         self.assertEqual(local.tip(), peer.tip())
         self.assertEqual(local.forks, peer.forks)
         self.assertEqual(set(local.ledger_state.keys()), set(peer.ledger_state.keys()))
 
     def test_sync_from_dishonest_checkpoint(self):
+        # Prepare multiple peers and a dishonest checkpoint:
         # Peer0: b0 - b1 - b2 - b5 == tip
         #           \
         # Peer1:      b3 - b4
@@ -269,17 +383,119 @@ class TestSyncFromCheckpoint(TestCase):
         self.assertEqual(peer1.tip(), b4)
         self.assertEqual(peer1.forks, [])
 
-        # Start from the checkpoint:
+        # Start a sync from the dishonest checkpoint:
         #       checkpoint
         #           ||
         # () - () - b4
+        #
+        # Result: The honest chain is found evetually by backfilling.
+        # b0 - b1 - b2 - b5 == tip
+        #    \
+        #      b3 - b4
         checkpoint = peer1.ledger_state[b4.id()]
         local = Follower(genesis, config)
         local.apply_checkpoint(checkpoint)
         sync(local, [peer0, peer1])
-        # b0 - b1 - b2 - b5 == tip
-        #    \
-        #      b3 - b4
         self.assertEqual(local.tip(), b5)
         self.assertEqual(local.forks, [b4.id()])
         self.assertEqual(len(local.ledger_state.keys()), 7)
+
+    def test_reject_invalid_blocks_from_backfilling_fork(self):
+        # Prepare a peer with invalid blocks in a fork:
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2 - (invalid_b6) - (invalid_b7)
+        #
+        # First, build a valid chain (b0 ~ b5):
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b3, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b4, c_a = mk_block(b3, 4, c_a), c_a.evolve()
+        b5, c_a = mk_block(b4, 5, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # And deliberately, add invalid blocks (b6 ~ b7):
+        fake_coin = Coin(sk=2, value=10)
+        b6, fake_coin = mk_block(b2, 3, fake_coin), fake_coin.evolve()
+        b7, fake_coin = mk_block(b6, 4, fake_coin), fake_coin.evolve()
+        apply_invalid_block_to_ledger_state(peer, b6)
+        apply_invalid_block_to_ledger_state(peer, b7)
+        # the tip shouldn't be changed.
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # Start a sync from a checkpoint where all anscestors are valid:
+        #            checkpoint
+        #                ||
+        # () - () - () - b4
+        #
+        # Result: A fork is backfilled, but without invalid blocks.
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2
+        checkpoint = peer.ledger_state[b4.id()]
+        local = Follower(genesis, config)
+        local.apply_checkpoint(checkpoint)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+        self.assertNotIn(b6.id(), local.ledger_state)
+        self.assertNotIn(b7.id(), local.ledger_state)
+
+    def test_reject_invalid_blocks_from_backfilling_block_tree(self):
+        # Prepare a peer with invalid blocks in a fork:
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2 - (invalid_b6) - (invalid_b7)
+        #
+        # First, build a valid chain (b0 ~ b5):
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b3, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b4, c_a = mk_block(b3, 4, c_a), c_a.evolve()
+        b5, c_a = mk_block(b4, 5, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # And deliberately, add invalid blocks (b6 ~ b7):
+        fake_coin = Coin(sk=2, value=10)
+        b6, fake_coin = mk_block(b2, 3, fake_coin), fake_coin.evolve()
+        b7, fake_coin = mk_block(b6, 4, fake_coin), fake_coin.evolve()
+        apply_invalid_block_to_ledger_state(peer, b6)
+        apply_invalid_block_to_ledger_state(peer, b7)
+        # the tip shouldn't be changed.
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # Start a sync from a checkpoint where some anscestors are invalid:
+        # ()          checkpoint
+        #   \             ||
+        #   () - () - (invalid_b7)
+        #
+        # Result: `InvalidBlockTree` exception
+        checkpoint = peer.ledger_state[b7.id()]
+        local = Follower(genesis, config)
+        local.apply_checkpoint(checkpoint)
+        with self.assertRaises(InvalidBlockTree):
+            sync(local, [peer])
+
+
+def apply_invalid_block_to_ledger_state(follower: Follower, block: BlockHeader):
+    state = follower.ledger_state[block.parent].copy()
+    state.apply(block)
+    follower.ledger_state[block.id()] = state