diff --git a/src/supernova/circuit.rs b/src/supernova/circuit.rs
index 21eecd4e..6716d19b 100644
--- a/src/supernova/circuit.rs
+++ b/src/supernova/circuit.rs
@@ -261,13 +261,16 @@ impl<'a, G: Group, SC: EnforcingStepCircuit<G::Base>> SuperNovaAugmentedCircuit<
   ) -> Result<Vec<AllocatedRelaxedR1CSInstance<G>>, SynthesisError> {
     let mut cs = cs.namespace(|| "alloc U_i default");
 
+    // Allocate a default relaxed r1cs instance
+    let default = AllocatedRelaxedR1CSInstance::default(
+      cs.namespace(|| "Allocate primary U_default".to_string()),
+      self.params.limb_width,
+      self.params.n_limbs,
+    )?;
+
     // The primary circuit just initialize single AllocatedRelaxedR1CSInstance
     let U_default = if self.params.is_primary_circuit {
-      vec![AllocatedRelaxedR1CSInstance::default(
-        cs.namespace(|| "Allocate primary U_default".to_string()),
-        self.params.limb_width,
-        self.params.n_limbs,
-      )?]
+      vec![default]
     } else {
       // The secondary circuit convert the incoming R1CS instance on index which match last_augmented_circuit_index
       let incoming_r1cs = AllocatedRelaxedR1CSInstance::from_r1cs_instance(
@@ -276,6 +279,7 @@ impl<'a, G: Group, SC: EnforcingStepCircuit<G::Base>> SuperNovaAugmentedCircuit<
         self.params.limb_width,
         self.params.n_limbs,
       )?;
+
       (0..num_augmented_circuits)
         .map(|i| {
           let i_alloc = alloc_const(
@@ -287,15 +291,10 @@ impl<'a, G: Group, SC: EnforcingStepCircuit<G::Base>> SuperNovaAugmentedCircuit<
             &i_alloc,
             last_augmented_circuit_index_checked,
           )?);
-          let default = &AllocatedRelaxedR1CSInstance::default(
-            cs.namespace(|| format!("Allocate U_default {:?}", i)),
-            self.params.limb_width,
-            self.params.n_limbs,
-          )?;
           conditionally_select_alloc_relaxed_r1cs(
             cs.namespace(|| format!("select on index namespace {:?}", i)),
             &incoming_r1cs,
-            default,
+            &default,
             &equal_bit,
           )
         })
diff --git a/src/supernova/test.rs b/src/supernova/test.rs
index 93c46747..7c367fea 100644
--- a/src/supernova/test.rs
+++ b/src/supernova/test.rs
@@ -655,7 +655,7 @@ fn test_recursive_circuit() {
   let ro_consts1: ROConstantsCircuit<G2> = PoseidonConstantsCircuit::default();
   let ro_consts2: ROConstantsCircuit<G1> = PoseidonConstantsCircuit::default();
 
-  test_recursive_circuit_with::<G1, G2>(&params1, &params2, ro_consts1, ro_consts2, 9835, 12028);
+  test_recursive_circuit_with::<G1, G2>(&params1, &params2, ro_consts1, ro_consts2, 9835, 12026);
 }
 
 fn test_pp_digest_with<G1, G2, T1, T2, NC>(non_uniform_circuit: &NC, expected: &str)
@@ -701,7 +701,7 @@ fn test_supernova_pp_digest() {
 
   test_pp_digest_with::<G1, G2, _, _, _>(
     &test_rom,
-    "232c6c75db09f58a6a5a67311422a937239f67233902f3804ed3484ae9cd2b03",
+    "4009cc520dac06aaecbe5e9ae9fd0d7a480f6c9bd4bd7c6a858afda055db0b00",
   );
 
   let rom = vec![
@@ -716,7 +716,7 @@ fn test_supernova_pp_digest() {
 
   test_pp_digest_with::<bn256::Point, grumpkin::Point, _, _, _>(
     &test_rom_grumpkin,
-    "5f1f389cffbb535fc6e7114a25ab4d0eed5457e98eb95c8a4720e48b83fc8701",
+    "057219a08592f69fe96c7bba05f89c5f840edf34d55ec38b51b03fe2fb3b4e00",
   );
 
   let rom = vec![
@@ -731,7 +731,7 @@ fn test_supernova_pp_digest() {
 
   test_pp_digest_with::<secp256k1::Point, secq256k1::Point, _, _, _>(
     &test_rom_secp,
-    "9ee20885d37d921673140bd9bfd6af06408b6d380a1e06f720990ea66d0f1e01",
+    "305a387d90fc600b8c715f49abf9042b775932b426d8c236c8c9ee5e36259e03",
   );
 }