diff --git a/codex-plonky2-circuits/src/circuits/utils.rs b/codex-plonky2-circuits/src/circuits/utils.rs
index 0fc910d..cd46e54 100644
--- a/codex-plonky2-circuits/src/circuits/utils.rs
+++ b/codex-plonky2-circuits/src/circuits/utils.rs
@@ -1,5 +1,6 @@
 use std::{fs, io};
 use std::path::Path;
+use itertools::Itertools;
 use plonky2::hash::hash_types::{HashOut, HashOutTarget, NUM_HASH_OUT_ELTS, RichField};
 use plonky2::iop::witness::{PartialWitness, WitnessWrite};
 use plonky2_field::extension::Extendable;
@@ -135,3 +136,14 @@ pub fn vec_to_array<const N: usize, T>(vec: Vec<T>) -> Result<[T; N]> {
         v.len()
     )))
 }
+
+/// Computes `if b { v0 } else { v1 }`.
+pub fn select_vec<
+    F: RichField + Extendable<D> + Poseidon2,
+    const D: usize,
+>(builder: &mut CircuitBuilder<F, D>, b: BoolTarget, v0: &[Target], v1: &[Target]) -> Vec<Target> {
+    v0.iter()
+        .zip_eq(v1)
+        .map(|(t0, t1)| builder.select(b, *t0, *t1))
+        .collect()
+}
diff --git a/codex-plonky2-circuits/src/recursion/tree2/node_circuit.rs b/codex-plonky2-circuits/src/recursion/tree2/node_circuit.rs
index 36668cb..3148476 100644
--- a/codex-plonky2-circuits/src/recursion/tree2/node_circuit.rs
+++ b/codex-plonky2-circuits/src/recursion/tree2/node_circuit.rs
@@ -10,7 +10,7 @@ use plonky2::plonk::proof::{ProofWithPublicInputs, ProofWithPublicInputsTarget};
 use plonky2_poseidon2::poseidon2_hash::poseidon2::Poseidon2;
 use crate::recursion::circuits::inner_circuit::InnerCircuit;
 use plonky2_field::extension::Extendable;
-use crate::circuits::utils::{select_hash, vec_to_array};
+use crate::circuits::utils::{select_hash, select_vec, vec_to_array};
 use crate::{error::CircuitError, Result};
 use crate::recursion::tree2::leaf_circuit::LeafCircuit;
 
@@ -78,6 +78,7 @@ impl<
 
         // circuit data for leaf
         let leaf_circ_data = leaf_circuit.get_circuit_data::<C,H>()?;
+
         // common data for leaf
         let leaf_common = leaf_circ_data.common.clone();
 
@@ -94,8 +95,6 @@ impl<
             let inner_cyclic_pis = &leaf_proofs[i].public_inputs;
             leaf_pub_input_hashes.extend_from_slice(&inner_cyclic_pis[0..4]);
         }
-        // hash the public input so H(H_0, ..., H_N)
-        let leaf_pub_input_hash = builder.hash_n_to_hash_no_pad::<H>(leaf_pub_input_hashes);
 
         // leaf verifier data
         // TODO: double check that it is ok for this verifier data to be private/witness
@@ -140,11 +139,11 @@ impl<
             let inner_cyclic_pis = &inner_cyclic_proof_with_pis[i].public_inputs;
             inner_pub_input_hashes.extend_from_slice(&inner_cyclic_pis[0..4]);
         }
-        // hash all the node public input h = H(h_1 | h_2 | ... | h_N)
-        // TODO: optimize by removing the need for 2 hashes and instead select then hash
-        let inner_pub_input_hash = builder.hash_n_to_hash_no_pad::<H>(inner_pub_input_hashes);
 
-        let node_hash_or_leaf_hash = select_hash(&mut builder, condition, leaf_pub_input_hash, inner_pub_input_hash);
+        // select the public input - either leaf or node
+        let pub_input_to_be_hashed = select_vec(&mut builder, condition, &leaf_pub_input_hashes ,&inner_pub_input_hashes);
+        // hash all the node public input h = H(h_1 | h_2 | ... | h_N)
+        let node_hash_or_leaf_hash= builder.hash_n_to_hash_no_pad::<H>(pub_input_to_be_hashed);
 
         builder.connect_hashes(pub_input_hash,node_hash_or_leaf_hash);