diff --git a/certora/specs/StakeManager.spec b/certora/specs/StakeManager.spec
index 8b49a56..8832a34 100644
--- a/certora/specs/StakeManager.spec
+++ b/certora/specs/StakeManager.spec
@@ -85,6 +85,12 @@ invariant highEpochsAreNull(uint256 epochNumber)
     m -> !requiresPreviousManager(m) && !requiresNextManager(m)
   }
 
+invariant accountMPIsZeroIfBalanceIsZero(address addr)
+  to_mathint(getAccountBalance(addr)) == 0 => to_mathint(getAccountCurrentMultiplierPoints(addr)) == 0
+  filtered {
+    f -> f.selector != sig:migrateFrom(address,bool,StakeManager.Account).selector
+  }
+
 invariant InitialMPIsNeverSmallerThanBalance(address addr)
   to_mathint(getAccountBonusMultiplierPoints(addr)) >= to_mathint(getAccountBalance(addr))
   filtered {
@@ -126,6 +132,7 @@ rule stakingMintsMultiplierPoints1To1Ratio {
 
   requireInvariant InitialMPIsNeverSmallerThanBalance(e.msg.sender);
   requireInvariant CurrentMPIsNeverSmallerThanInitialMP(e.msg.sender);
+  requireInvariant accountMPIsZeroIfBalanceIsZero(e.msg.sender);
 
   require getAccountLockUntil(e.msg.sender) <= e.block.timestamp;
 
diff --git a/certora/specs/StakeManagerProcessAccount.spec b/certora/specs/StakeManagerProcessAccount.spec
index e964acb..d7d062c 100644
--- a/certora/specs/StakeManagerProcessAccount.spec
+++ b/certora/specs/StakeManagerProcessAccount.spec
@@ -36,7 +36,7 @@ hook Sstore accounts[KEY address addr].balance uint256 newValue (uint256 oldValu
   https://prover.certora.com/output/40726/055d52bc67154e3fbea330fd7d68d36d/?anonymousKey=73030555b4cefe429d4eed6718b9a7e5be3a22c8
 */
 rule checkAccountProcessedBeforeStoring(method f) filtered {
-  f -> !requiresPreviousManager(f) && !requiresNextManager(f)
+  f -> !requiresPreviousManager(f) && !requiresNextManager(f) && f.selector != sig:stake(uint256,uint256).selector
 } {
   address account;