diff --git a/src/fri/recursive_verifier.rs b/src/fri/recursive_verifier.rs
index 12246504..11cdd7d4 100644
--- a/src/fri/recursive_verifier.rs
+++ b/src/fri/recursive_verifier.rs
@@ -33,13 +33,9 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         // The evaluation vector needs to be reordered first.
         let mut evals = last_evals.to_vec();
         reverse_index_bits_in_place(&mut evals);
-        let mut old_x_index_bits = old_x_index_bits.to_vec();
-        old_x_index_bits.reverse();
         // Want `g^(arity - rev_old_x_index)` as in the out-of-circuit version.
         // Compute it as `g^(arity-1-rev_old_x_index) * g`, where the first term is gotten using two's complement.
-        // TODO: Once the exponentiation gate lands, we won't need the bits and will be able to compute
-        // `g^(arity-rev_old_x_index)` directly.
-        let start = self.exp_from_complement_bits(gt, &old_x_index_bits);
+        let start = self.exp_from_complement_bits(gt, old_x_index_bits.iter().rev());
         let coset_start = self.mul_many(&[start, gt, x]);
 
         // The answer is gotten by interpolating {(x*g^i, P(x*g^i))} and evaluating at beta.
diff --git a/src/gadgets/arithmetic.rs b/src/gadgets/arithmetic.rs
index 6dcf1b3d..0598f3e7 100644
--- a/src/gadgets/arithmetic.rs
+++ b/src/gadgets/arithmetic.rs
@@ -1,3 +1,5 @@
+use std::borrow::Borrow;
+
 use crate::circuit_builder::CircuitBuilder;
 use crate::field::extension_field::Extendable;
 use crate::target::Target;
@@ -187,15 +189,19 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     // TODO: Optimize this, maybe with a new gate.
     // TODO: Test
     /// Exponentiate `base` to the power of `2^bit_length-1-exponent`, given by its little-endian bits.
-    pub fn exp_from_complement_bits(&mut self, base: Target, exponent_bits: &[Target]) -> Target {
+    pub fn exp_from_complement_bits(
+        &mut self,
+        base: Target,
+        exponent_bits: impl ExactSizeIterator<Item = impl Borrow<Target>> + Clone,
+    ) -> Target {
         let mut current = base;
         let one_ext = self.one_extension();
         let mut product = self.one();
 
-        for &bit in exponent_bits {
+        for bit in exponent_bits {
             let current_ext = self.convert_to_ext(current);
             // TODO: Add base field select.
-            let multiplicand = self.select(bit, one_ext, current_ext);
+            let multiplicand = self.select(*bit.borrow(), one_ext, current_ext);
             product = self.mul(product, multiplicand.0[0]);
             current = self.mul(current, current);
         }