diff --git a/src/fri/proof.rs b/src/fri/proof.rs
index 4ee5bafb..9751825f 100644
--- a/src/fri/proof.rs
+++ b/src/fri/proof.rs
@@ -1,18 +1,22 @@
+use std::collections::hash_map::Entry::Vacant;
+
 use serde::{Deserialize, Serialize};
 
 use crate::field::extension_field::target::ExtensionTarget;
-use crate::field::extension_field::Extendable;
-use crate::field::field_types::Field;
+use crate::field::extension_field::{flatten, unflatten, Extendable};
+use crate::field::field_types::{Field, RichField};
 use crate::gadgets::polynomial::PolynomialCoeffsExtTarget;
 use crate::hash::hash_types::MerkleCapTarget;
 use crate::hash::merkle_proofs::{MerkleProof, MerkleProofTarget};
 use crate::hash::merkle_tree::MerkleCap;
+use crate::hash::path_compression::{compress_merkle_proofs, decompress_merkle_proofs};
 use crate::iop::target::Target;
+use crate::plonk::circuit_data::CommonCircuitData;
 use crate::plonk::plonk_common::PolynomialsIndexBlinding;
 use crate::polynomial::polynomial::PolynomialCoeffs;
 
 /// Evaluations and Merkle proof produced by the prover in a FRI query step.
-#[derive(Serialize, Deserialize, Clone, Debug)]
+#[derive(Serialize, Deserialize, Clone, Debug, Eq, PartialEq)]
 #[serde(bound = "")]
 pub struct FriQueryStep<F: Extendable<D>, const D: usize> {
     pub evals: Vec<F::Extension>,
@@ -27,7 +31,7 @@ pub struct FriQueryStepTarget<const D: usize> {
 
 /// Evaluations and Merkle proofs of the original set of polynomials,
 /// before they are combined into a composition polynomial.
-#[derive(Serialize, Deserialize, Clone, Debug)]
+#[derive(Serialize, Deserialize, Clone, Debug, Eq, PartialEq)]
 #[serde(bound = "")]
 pub struct FriInitialTreeProof<F: Field> {
     pub evals_proofs: Vec<(Vec<F>, MerkleProof<F>)>,
@@ -61,9 +65,10 @@ impl FriInitialTreeProofTarget {
 }
 
 /// Proof for a FRI query round.
-#[derive(Serialize, Deserialize, Clone, Debug)]
+#[derive(Serialize, Deserialize, Clone, Debug, Eq, PartialEq)]
 #[serde(bound = "")]
 pub struct FriQueryRound<F: Extendable<D>, const D: usize> {
+    pub index: usize,
     pub initial_trees_proof: FriInitialTreeProof<F>,
     pub steps: Vec<FriQueryStep<F, D>>,
 }
@@ -74,7 +79,7 @@ pub struct FriQueryRoundTarget<const D: usize> {
     pub steps: Vec<FriQueryStepTarget<D>>,
 }
 
-#[derive(Serialize, Deserialize, Clone, Debug)]
+#[derive(Serialize, Deserialize, Clone, Debug, Eq, PartialEq)]
 #[serde(bound = "")]
 pub struct FriProof<F: Extendable<D>, const D: usize> {
     /// A Merkle cap for each reduced polynomial in the commit phase.
@@ -85,6 +90,8 @@ pub struct FriProof<F: Extendable<D>, const D: usize> {
     pub final_poly: PolynomialCoeffs<F::Extension>,
     /// Witness showing that the prover did PoW.
     pub pow_witness: F,
+    /// Flag set to true if path compression has been applied to the proof's Merkle proofs.
+    pub is_compressed: bool,
 }
 
 pub struct FriProofTarget<const D: usize> {
@@ -93,3 +100,186 @@ pub struct FriProofTarget<const D: usize> {
     pub final_poly: PolynomialCoeffsExtTarget<D>,
     pub pow_witness: Target,
 }
+
+impl<F: RichField + Extendable<D>, const D: usize> FriProof<F, D> {
+    pub fn compress(self, common_data: &CommonCircuitData<F, D>) -> Self {
+        if self.is_compressed {
+            panic!("Proof is already compressed.");
+        }
+        let FriProof {
+            commit_phase_merkle_caps,
+            mut query_round_proofs,
+            final_poly,
+            pow_witness,
+            ..
+        } = self;
+        let cap_height = common_data.config.cap_height;
+        let reduction_arity_bits = &common_data.config.fri_config.reduction_arity_bits;
+        let num_reductions = reduction_arity_bits.len();
+        let num_initial_trees = query_round_proofs[0].initial_trees_proof.evals_proofs.len();
+
+        // "Transpose" the query round proofs, so that information for each Merkle tree is collected together.
+        let mut initial_trees_indices = vec![vec![]; num_initial_trees];
+        let mut initial_trees_leaves = vec![vec![]; num_initial_trees];
+        let mut initial_trees_proofs = vec![vec![]; num_initial_trees];
+        let mut steps_indices = vec![vec![]; num_reductions];
+        let mut steps_evals = vec![vec![]; num_reductions];
+        let mut steps_proofs = vec![vec![]; num_reductions];
+
+        for qrp in &query_round_proofs {
+            let FriQueryRound {
+                mut index,
+                initial_trees_proof,
+                steps,
+            } = qrp.clone();
+            for (i, (leaves_data, proof)) in
+                initial_trees_proof.evals_proofs.into_iter().enumerate()
+            {
+                initial_trees_indices[i].push(index);
+                initial_trees_leaves[i].push(leaves_data);
+                initial_trees_proofs[i].push(proof);
+            }
+            for (i, query_step) in steps.into_iter().enumerate() {
+                index >>= reduction_arity_bits[i];
+                steps_indices[i].push(index);
+                steps_evals[i].push(query_step.evals);
+                steps_proofs[i].push(query_step.merkle_proof);
+            }
+        }
+
+        // Compress all Merkle proofs.
+        let initial_trees_proofs = initial_trees_indices
+            .iter()
+            .zip(initial_trees_proofs)
+            .map(|(is, ps)| compress_merkle_proofs(cap_height, is, &ps))
+            .collect::<Vec<_>>();
+        let steps_proofs = steps_indices
+            .iter()
+            .zip(steps_proofs)
+            .map(|(is, ps)| compress_merkle_proofs(cap_height, is, &ps))
+            .collect::<Vec<_>>();
+
+        for (i, qrp) in query_round_proofs.iter_mut().enumerate() {
+            qrp.initial_trees_proof = FriInitialTreeProof {
+                evals_proofs: (0..num_initial_trees)
+                    .map(|j| {
+                        (
+                            initial_trees_leaves[j][i].clone(),
+                            initial_trees_proofs[j][i].clone(),
+                        )
+                    })
+                    .collect(),
+            };
+            qrp.steps = (0..num_reductions)
+                .map(|j| FriQueryStep {
+                    evals: steps_evals[j][i].clone(),
+                    merkle_proof: steps_proofs[j][i].clone(),
+                })
+                .collect();
+        }
+
+        FriProof {
+            commit_phase_merkle_caps,
+            query_round_proofs,
+            final_poly,
+            pow_witness,
+            is_compressed: true,
+        }
+    }
+
+    pub fn decompress(self, common_data: &CommonCircuitData<F, D>) -> Self {
+        if !self.is_compressed {
+            panic!("Proof is not compressed.");
+        }
+        let FriProof {
+            commit_phase_merkle_caps,
+            mut query_round_proofs,
+            final_poly,
+            pow_witness,
+            ..
+        } = self;
+        let cap_height = common_data.config.cap_height;
+        let reduction_arity_bits = &common_data.config.fri_config.reduction_arity_bits;
+        let num_reductions = reduction_arity_bits.len();
+        let num_initial_trees = query_round_proofs[0].initial_trees_proof.evals_proofs.len();
+
+        // "Transpose" the query round proofs, so that information for each Merkle tree is collected together.
+        let mut initial_trees_indices = vec![vec![]; num_initial_trees];
+        let mut initial_trees_leaves = vec![vec![]; num_initial_trees];
+        let mut initial_trees_proofs = vec![vec![]; num_initial_trees];
+        let mut steps_indices = vec![vec![]; num_reductions];
+        let mut steps_evals = vec![vec![]; num_reductions];
+        let mut steps_proofs = vec![vec![]; num_reductions];
+        let height = common_data.degree_bits + common_data.config.rate_bits;
+        let heights = reduction_arity_bits
+            .iter()
+            .scan(height, |acc, &bits| {
+                *acc -= bits;
+                Some(*acc)
+            })
+            .collect::<Vec<_>>();
+
+        for qrp in &query_round_proofs {
+            let FriQueryRound {
+                mut index,
+                initial_trees_proof,
+                steps,
+            } = qrp.clone();
+            for (i, (leaves_data, proof)) in
+                initial_trees_proof.evals_proofs.into_iter().enumerate()
+            {
+                initial_trees_indices[i].push(index);
+                initial_trees_leaves[i].push(leaves_data);
+                initial_trees_proofs[i].push(proof);
+            }
+            for (i, query_step) in steps.into_iter().enumerate() {
+                index >>= reduction_arity_bits[i];
+                steps_indices[i].push(index);
+                steps_evals[i].push(flatten(&query_step.evals));
+                steps_proofs[i].push(query_step.merkle_proof);
+            }
+        }
+
+        // Compress all Merkle proofs.
+        let initial_trees_proofs = initial_trees_leaves
+            .iter()
+            .zip(&initial_trees_indices)
+            .zip(initial_trees_proofs)
+            .map(|((ls, is), ps)| decompress_merkle_proofs(&ls, is, &ps, height, cap_height))
+            .collect::<Vec<_>>();
+        let steps_proofs = steps_evals
+            .iter()
+            .zip(&steps_indices)
+            .zip(steps_proofs)
+            .zip(heights)
+            .map(|(((ls, is), ps), h)| decompress_merkle_proofs(ls, is, &ps, h, cap_height))
+            .collect::<Vec<_>>();
+
+        for (i, qrp) in query_round_proofs.iter_mut().enumerate() {
+            qrp.initial_trees_proof = FriInitialTreeProof {
+                evals_proofs: (0..num_initial_trees)
+                    .map(|j| {
+                        (
+                            initial_trees_leaves[j][i].clone(),
+                            initial_trees_proofs[j][i].clone(),
+                        )
+                    })
+                    .collect(),
+            };
+            qrp.steps = (0..num_reductions)
+                .map(|j| FriQueryStep {
+                    evals: unflatten(&steps_evals[j][i]),
+                    merkle_proof: steps_proofs[j][i].clone(),
+                })
+                .collect();
+        }
+
+        FriProof {
+            commit_phase_merkle_caps,
+            query_round_proofs,
+            final_poly,
+            pow_witness,
+            is_compressed: false,
+        }
+    }
+}
diff --git a/src/fri/prover.rs b/src/fri/prover.rs
index a0d71d98..6bc0562a 100644
--- a/src/fri/prover.rs
+++ b/src/fri/prover.rs
@@ -63,6 +63,7 @@ pub fn fri_proof<F: RichField + Extendable<D>, const D: usize>(
         query_round_proofs,
         final_poly: final_coeffs,
         pow_witness,
+        is_compressed: false,
     }
 }
 
@@ -152,7 +153,8 @@ fn fri_prover_query_round<F: RichField + Extendable<D>, const D: usize>(
 ) -> FriQueryRound<F, D> {
     let mut query_steps = Vec::new();
     let x = challenger.get_challenge();
-    let mut x_index = x.to_canonical_u64() as usize % n;
+    let initial_index = x.to_canonical_u64() as usize % n;
+    let mut x_index = initial_index;
     let initial_proof = initial_merkle_trees
         .iter()
         .map(|t| (t.get(x_index).to_vec(), t.prove(x_index)))
@@ -170,6 +172,7 @@ fn fri_prover_query_round<F: RichField + Extendable<D>, const D: usize>(
         x_index >>= arity_bits;
     }
     FriQueryRound {
+        index: initial_index,
         initial_trees_proof: FriInitialTreeProof {
             evals_proofs: initial_proof,
         },
diff --git a/src/fri/verifier.rs b/src/fri/verifier.rs
index e14e586f..20579da7 100644
--- a/src/fri/verifier.rs
+++ b/src/fri/verifier.rs
@@ -259,6 +259,7 @@ fn fri_verifier_query_round<F: RichField + Extendable<D>, const D: usize>(
     let config = &common_data.config.fri_config;
     let x = challenger.get_challenge();
     let mut x_index = x.to_canonical_u64() as usize % n;
+    ensure!(x_index == round_proof.index, "Wrong index.");
     fri_verify_initial_proof(
         x_index,
         &round_proof.initial_trees_proof,
diff --git a/src/gadgets/arithmetic_extension.rs b/src/gadgets/arithmetic_extension.rs
index af838ab6..4645e38f 100644
--- a/src/gadgets/arithmetic_extension.rs
+++ b/src/gadgets/arithmetic_extension.rs
@@ -601,6 +601,10 @@ mod tests {
 
         let data = builder.build();
         let proof = data.prove(pw)?;
+        let mut go = proof.proof.opening_proof.clone();
+        let goc = go.clone().compress(&data.common);
+        let gocd = goc.decompress(&data.common);
+        assert_eq!(go, gocd);
 
         verify(proof, &data.verifier_only, &data.common)
     }
diff --git a/src/hash/merkle_tree.rs b/src/hash/merkle_tree.rs
index f512a260..9b9ffe7e 100644
--- a/src/hash/merkle_tree.rs
+++ b/src/hash/merkle_tree.rs
@@ -8,7 +8,7 @@ use crate::hash::merkle_proofs::MerkleProof;
 
 /// The Merkle cap of height `h` of a Merkle tree is the `h`-th layer (from the root) of the tree.
 /// It can be used in place of the root to verify Merkle paths, which are `h` elements shorter.
-#[derive(Clone, Debug, Serialize, Deserialize)]
+#[derive(Clone, Debug, Serialize, Deserialize, Eq, PartialEq)]
 #[serde(bound = "")]
 pub struct MerkleCap<F: Field>(pub Vec<HashOut<F>>);
 
diff --git a/src/hash/path_compression.rs b/src/hash/path_compression.rs
index cb6cd8e1..38b8543c 100644
--- a/src/hash/path_compression.rs
+++ b/src/hash/path_compression.rs
@@ -14,25 +14,26 @@ use crate::util::log2_strict;
 /// Compress multiple Merkle proofs on the same tree by removing redundancy in the Merkle paths.
 pub(crate) fn compress_merkle_proofs<F: Field>(
     cap_height: usize,
-    proofs: Vec<(usize, MerkleProof<F>)>,
+    indices: &[usize],
+    proofs: &[MerkleProof<F>],
 ) -> Vec<MerkleProof<F>> {
     assert!(!proofs.is_empty());
-    let height = cap_height + proofs[0].1.siblings.len();
+    let height = cap_height + proofs[0].siblings.len();
     let num_leaves = 1 << height;
     let mut compressed_proofs = Vec::with_capacity(proofs.len());
     // Holds the known nodes in the tree at a given time. The root is at index 1.
     let mut known = vec![false; 2 * num_leaves];
-    for (i, _) in &proofs {
+    for &i in indices {
         // The leaves are known.
-        known[*i + num_leaves] = true;
+        known[i + num_leaves] = true;
     }
     // For each proof collect all the unknown proof elements.
-    for (i, p) in proofs {
+    for (&i, p) in indices.iter().zip(proofs) {
         let mut compressed_proof = MerkleProof {
             siblings: Vec::new(),
         };
         let mut index = i + num_leaves;
-        for sibling in p.siblings {
+        for &sibling in &p.siblings {
             let sibling_index = index ^ 1;
             if !known[sibling_index] {
                 // If the sibling is not yet known, add it to the proof and set it to known.
@@ -51,15 +52,14 @@ pub(crate) fn compress_merkle_proofs<F: Field>(
 
 /// Verify a compressed Merkle proof.
 /// Note: The data and indices must be in the same order as in `compress_merkle_proofs`.
-pub(crate) fn decompress_merkle_proof<F: RichField>(
+pub(crate) fn decompress_merkle_proofs<F: RichField>(
     leaves_data: &[Vec<F>],
     leaves_indices: &[usize],
     compressed_proofs: &[MerkleProof<F>],
     height: usize,
-    cap: &MerkleCap<F>,
+    cap_height: usize,
 ) -> Vec<MerkleProof<F>> {
     let num_leaves = 1 << height;
-    let cap_height = log2_strict(cap.len());
     let mut compressed_proofs = compressed_proofs.to_vec();
     let mut decompressed_proofs = Vec::with_capacity(compressed_proofs.len());
     // Holds the already seen nodes in the tree along with their value.
@@ -124,19 +124,17 @@ mod tests {
         let mut rng = thread_rng();
         let k = rng.gen_range(1..=1 << h);
         let indices = (0..k).map(|_| rng.gen_range(0..1 << h)).collect::<Vec<_>>();
-        let proofs: Vec<(usize, MerkleProof<_>)> =
-            indices.iter().map(|&i| (i, mt.prove(i))).collect();
+        let proofs = indices.iter().map(|&i| mt.prove(i)).collect::<Vec<_>>();
 
-        let compressed_proofs = compress_merkle_proofs(cap_height, proofs.clone());
-        let decompressed_proofs = decompress_merkle_proof(
+        let compressed_proofs = compress_merkle_proofs(cap_height, &indices, &proofs);
+        let decompressed_proofs = decompress_merkle_proofs(
             &indices.iter().map(|&i| vs[i].clone()).collect::<Vec<_>>(),
             &indices,
             &compressed_proofs,
             h,
-            &mt.cap,
+            cap_height,
         );
 
-        let proofs = proofs.into_iter().map(|(_, p)| p).collect::<Vec<_>>();
         assert_eq!(proofs, decompressed_proofs);
 
         let compressed_proof_bytes = serde_cbor::to_vec(&compressed_proofs).unwrap();
diff --git a/src/plonk/proof.rs b/src/plonk/proof.rs
index 68871202..06a7f3ed 100644
--- a/src/plonk/proof.rs
+++ b/src/plonk/proof.rs
@@ -26,13 +26,6 @@ pub struct Proof<F: Extendable<D>, const D: usize> {
     pub opening_proof: FriProof<F, D>,
 }
 
-#[derive(Serialize, Deserialize, Clone, Debug)]
-#[serde(bound = "")]
-pub struct ProofWithPublicInputs<F: Extendable<D>, const D: usize> {
-    pub proof: Proof<F, D>,
-    pub public_inputs: Vec<F>,
-}
-
 pub struct ProofTarget<const D: usize> {
     pub wires_cap: MerkleCapTarget,
     pub plonk_zs_partial_products_cap: MerkleCapTarget,
@@ -41,11 +34,50 @@ pub struct ProofTarget<const D: usize> {
     pub opening_proof: FriProofTarget<D>,
 }
 
+impl<F: RichField + Extendable<D>, const D: usize> Proof<F, D> {
+    pub fn is_compressed(&self) -> bool {
+        self.opening_proof.is_compressed
+    }
+
+    pub fn compress(mut self, common_data: &CommonCircuitData<F, D>) -> Self {
+        self.opening_proof = self.opening_proof.compress(common_data);
+        self
+    }
+
+    pub fn decompress(mut self, common_data: &CommonCircuitData<F, D>) -> Self {
+        self.opening_proof = self.opening_proof.decompress(common_data);
+        self
+    }
+}
+
+#[derive(Serialize, Deserialize, Clone, Debug)]
+#[serde(bound = "")]
+pub struct ProofWithPublicInputs<F: Extendable<D>, const D: usize> {
+    pub proof: Proof<F, D>,
+    pub public_inputs: Vec<F>,
+}
+
 pub struct ProofWithPublicInputsTarget<const D: usize> {
     pub proof: ProofTarget<D>,
     pub public_inputs: Vec<Target>,
 }
 
+impl<F: RichField + Extendable<D>, const D: usize> ProofWithPublicInputs<F, D> {
+    pub fn is_compressed(&self) -> bool {
+        self.proof.is_compressed()
+    }
+
+    pub fn compress(mut self, common_data: &CommonCircuitData<F, D>) -> Self {
+        self.proof = self.proof.compress(common_data);
+        self
+    }
+
+    pub fn decompress(mut self, common_data: &CommonCircuitData<F, D>) -> Self {
+        self.proof = self.proof.decompress(common_data);
+        self
+    }
+}
+
 #[derive(Clone, Debug, Serialize, Deserialize)]
 /// The purported values of each polynomial at a single point.
 pub struct OpeningSet<F: Extendable<D>, const D: usize> {
diff --git a/src/plonk/recursive_verifier.rs b/src/plonk/recursive_verifier.rs
index 0b371b9d..98d5d7cc 100644
--- a/src/plonk/recursive_verifier.rs
+++ b/src/plonk/recursive_verifier.rs
@@ -479,8 +479,16 @@ mod tests {
         builder.print_gate_counts(0);
         let data = builder.build();
         let recursive_proof = data.prove(pw)?;
+        let now = std::time::Instant::now();
+        let compressed_recursive_proof = recursive_proof.clone().compress(&data.common);
+        info!("{:.4} to compress proof", now.elapsed().as_secs_f64());
         let proof_bytes = serde_cbor::to_vec(&recursive_proof).unwrap();
         info!("Proof length: {} bytes", proof_bytes.len());
+        let compressed_proof_bytes = serde_cbor::to_vec(&compressed_recursive_proof).unwrap();
+        info!(
+            "Compressed proof length: {} bytes",
+            compressed_proof_bytes.len()
+        );
         verify(recursive_proof, &data.verifier_only, &data.common)
     }
 }
diff --git a/src/plonk/verifier.rs b/src/plonk/verifier.rs
index 96c43d52..217e5cb4 100644
--- a/src/plonk/verifier.rs
+++ b/src/plonk/verifier.rs
@@ -12,10 +12,14 @@ use crate::plonk::vanishing_poly::eval_vanishing_poly;
 use crate::plonk::vars::EvaluationVars;
 
 pub(crate) fn verify<F: RichField + Extendable<D>, const D: usize>(
-    proof_with_pis: ProofWithPublicInputs<F, D>,
+    mut proof_with_pis: ProofWithPublicInputs<F, D>,
     verifier_data: &VerifierOnlyCircuitData<F>,
     common_data: &CommonCircuitData<F, D>,
 ) -> Result<()> {
+    // Decompress the proof if needed.
+    if proof_with_pis.is_compressed() {
+        proof_with_pis = proof_with_pis.decompress(common_data);
+    }
     let ProofWithPublicInputs {
         proof,
         public_inputs,