diff --git a/integration_tests/tests/auth_transfer/private.rs b/integration_tests/tests/auth_transfer/private.rs
index 8136f9df..a472c260 100644
--- a/integration_tests/tests/auth_transfer/private.rs
+++ b/integration_tests/tests/auth_transfer/private.rs
@@ -81,7 +81,7 @@ async fn private_transfer_to_foreign_account() -> Result<()> {
         .context("Failed to get private account commitment for sender")?;
 
     let tx = fetch_privacy_preserving_tx(ctx.sequencer_client(), tx_hash).await;
-    assert_eq!(tx.message.new_commitments[0], new_commitment1);
+    assert!(tx.message.new_commitments.contains(&new_commitment1));
 
     for commitment in tx.message.new_commitments {
         assert!(verify_commitment_is_in_state(commitment, ctx.sequencer_client()).await);
@@ -169,7 +169,7 @@ async fn private_transfer_to_owned_account_using_claiming_path() -> Result<()> {
         .wallet()
         .get_private_account_commitment(from)
         .context("Failed to get private account commitment for sender")?;
-    assert_eq!(tx.message.new_commitments[0], sender_commitment);
+    assert!(tx.message.new_commitments.contains(&sender_commitment));
 
     for commitment in tx.message.new_commitments {
         assert!(verify_commitment_is_in_state(commitment, ctx.sequencer_client()).await);
@@ -245,13 +245,9 @@ async fn shielded_transfer_to_foreign_account() -> Result<()> {
 
     let acc_1_balance = account_balance(&ctx, from).await?;
 
-    assert!(
-        verify_commitment_is_in_state(
-            tx.message.new_commitments[0].clone(),
-            ctx.sequencer_client()
-        )
-        .await
-    );
+    for commitment in tx.message.new_commitments {
+        assert!(verify_commitment_is_in_state(commitment, ctx.sequencer_client()).await);
+    }
 
     assert_eq!(acc_1_balance, 9900);
 
diff --git a/integration_tests/tests/keys.rs b/integration_tests/tests/keys.rs
index f0a66e0e..fb958ec0 100644
--- a/integration_tests/tests/keys.rs
+++ b/integration_tests/tests/keys.rs
@@ -71,7 +71,7 @@ async fn sync_private_account_with_non_zero_chain_index() -> Result<()> {
         .wallet()
         .get_private_account_commitment(from)
         .context("Failed to get private account commitment for sender")?;
-    assert_eq!(tx.message.new_commitments[0], new_commitment1);
+    assert!(tx.message.new_commitments.contains(&new_commitment1));
 
     for commitment in tx.message.new_commitments {
         assert!(verify_commitment_is_in_state(commitment, ctx.sequencer_client()).await);
diff --git a/lee/state_machine/core/src/encryption/mod.rs b/lee/state_machine/core/src/encryption/mod.rs
index 3b244b5c..13ad7f5e 100644
--- a/lee/state_machine/core/src/encryption/mod.rs
+++ b/lee/state_machine/core/src/encryption/mod.rs
@@ -246,11 +246,19 @@ mod tests {
 
         // Wrong shared secret must not decrypt correctly.
         let wrong_ss = SharedSecretKey([0_u8; 32]);
-        let bad = EncryptionScheme::decrypt(&ct, &wrong_ss, &nullifier);
+        let bad_via_ss = EncryptionScheme::decrypt(&ct, &wrong_ss, &nullifier);
         assert!(
-            bad.is_none() || bad.is_some_and(|(_, a)| a.balance != 999),
+            bad_via_ss.is_none() || bad_via_ss.is_some_and(|(_, a)| a.balance != 999),
             "wrong shared secret must not produce the correct plaintext"
         );
+
+        // Wrong nullifier must not decrypt correctly.
+        let wrong_nullifier = Nullifier::for_account_initialization(&AccountId::new([9; 32]));
+        let bad_via_nlf = EncryptionScheme::decrypt(&ct, &receiver_ss, &wrong_nullifier);
+        assert!(
+            bad_via_nlf.is_none() || bad_via_nlf.is_some_and(|(_, a)| a.balance != 999),
+            "wrong nullifier must not produce the correct plaintext"
+        );
     }
 
     #[test]
diff --git a/lee/state_machine/src/privacy_preserving_transaction/circuit/tests.rs b/lee/state_machine/src/privacy_preserving_transaction/circuit/tests.rs
index 88494861..d5663b6d 100644
--- a/lee/state_machine/src/privacy_preserving_transaction/circuit/tests.rs
+++ b/lee/state_machine/src/privacy_preserving_transaction/circuit/tests.rs
@@ -218,22 +218,41 @@ fn prove_privacy_preserving_execution_circuit_fully_private() {
     assert!(proof.is_valid_for(&output));
     assert!(output.public_pre_states.is_empty());
     assert!(output.public_post_states.is_empty());
+    let sender_nullifier = expected_new_nullifiers[0].0;
+    let recipient_nullifier = expected_new_nullifiers[1].0;
+
+    let mut expected_new_commitments = expected_new_commitments;
+    expected_new_commitments.sort_unstable_by_key(Commitment::to_byte_array);
     assert_eq!(output.new_commitments, expected_new_commitments);
+
+    let mut expected_new_nullifiers = expected_new_nullifiers;
+    expected_new_nullifiers.sort_unstable_by_key(|(nullifier, _)| nullifier.to_byte_array());
     assert_eq!(output.new_nullifiers, expected_new_nullifiers);
+
     assert_eq!(output.encrypted_private_post_states.len(), 2);
 
+    let sender_slot = output
+        .new_nullifiers
+        .iter()
+        .position(|(nullifier, _)| *nullifier == sender_nullifier)
+        .unwrap();
     let (_identifier, sender_post) = EncryptionScheme::decrypt(
-        &output.encrypted_private_post_states[0].ciphertext,
+        &output.encrypted_private_post_states[sender_slot].ciphertext,
         &shared_secret_1,
-        &output.new_nullifiers[0].0,
+        &output.new_nullifiers[sender_slot].0,
     )
     .unwrap();
     assert_eq!(sender_post, expected_private_account_1);
 
+    let recipient_slot = output
+        .new_nullifiers
+        .iter()
+        .position(|(nullifier, _)| *nullifier == recipient_nullifier)
+        .unwrap();
     let (_identifier, recipient_post) = EncryptionScheme::decrypt(
-        &output.encrypted_private_post_states[1].ciphertext,
+        &output.encrypted_private_post_states[recipient_slot].ciphertext,
         &shared_secret_2,
-        &output.new_nullifiers[1].0,
+        &output.new_nullifiers[recipient_slot].0,
     )
     .unwrap();
     assert_eq!(recipient_post, expected_private_account_2);