diff --git a/src/fri/recursive_verifier.rs b/src/fri/recursive_verifier.rs
index 9b3cdd6e..7592bc1f 100644
--- a/src/fri/recursive_verifier.rs
+++ b/src/fri/recursive_verifier.rs
@@ -271,8 +271,7 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
             let g = self.constant(F::MULTIPLICATIVE_GROUP_GENERATOR);
             let phi = self.constant(F::primitive_root_of_unity(n_log));
 
-            let reversed_x = self.le_sum(x_index_bits.iter().rev());
-            let phi = self.exp(phi, reversed_x, n_log);
+            let phi = self.exp_from_bits(phi, x_index_bits.iter().rev());
             self.mul(g, phi)
         });
 
diff --git a/src/gadgets/arithmetic.rs b/src/gadgets/arithmetic.rs
index 7afa9319..cfeef82e 100644
--- a/src/gadgets/arithmetic.rs
+++ b/src/gadgets/arithmetic.rs
@@ -170,13 +170,17 @@ 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 `exponent`, given by its little-endian bits.
-    pub fn exp_from_bits(&mut self, base: Target, exponent_bits: &[Target]) -> Target {
+    pub fn exp_from_bits(
+        &mut self,
+        base: Target,
+        exponent_bits: impl Iterator<Item = impl Borrow<Target>>,
+    ) -> Target {
         let mut current = base;
         let one = self.one();
         let mut product = one;
 
-        for &bit in exponent_bits {
-            let multiplicand = self.select(bit, current, one);
+        for bit in exponent_bits {
+            let multiplicand = self.select(*bit.borrow(), current, one);
             product = self.mul(product, multiplicand);
             current = self.mul(current, current);
         }
@@ -210,7 +214,7 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     /// Exponentiate `base` to the power of `exponent`, where `exponent < 2^num_bits`.
     pub fn exp(&mut self, base: Target, exponent: Target, num_bits: usize) -> Target {
         let exponent_bits = self.split_le(exponent, num_bits);
-        self.exp_from_bits(base, &exponent_bits)
+        self.exp_from_bits(base, exponent_bits.iter())
     }
 
     /// Exponentiate `base` to the power of a known `exponent`.