diff --git a/src/fri/proof.rs b/src/fri/proof.rs
index 264e2e9e..03239629 100644
--- a/src/fri/proof.rs
+++ b/src/fri/proof.rs
@@ -169,6 +169,7 @@ impl<F: RichField + Extendable<D>, const D: usize> FriProof<F, D> {
                 index >>= reduction_arity_bits[i];
                 steps_indices[i].push(index);
                 let mut evals = query_step.evals;
+                // Remove the element that can be inferred.
                 evals.remove(index_within_coset);
                 steps_evals[i].push(evals);
                 steps_proofs[i].push(query_step.merkle_proof);
@@ -252,7 +253,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CompressedFriProof<F, D> {
         let mut fri_query_inferred_elements = if let Some(v) = fri_query_inferred_elements {
             v.iter().copied()
         } else {
-            panic!()
+            panic!("Proof challenges must be computed with `CompressedProofWithPublicInputs::get_challenges()`.")
         };
         let cap_height = common_data.config.cap_height;
         let reduction_arity_bits = &common_data.fri_params.reduction_arity_bits;
@@ -281,6 +282,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CompressedFriProof<F, D> {
             })
             .collect::<Vec<_>>();
 
+        // Holds the `evals` vectors that have already been reconstructed at each reduction depth.
         let mut evals_by_depth = vec![
             HashMap::<usize, Vec<_>>::new();
             common_data.fri_params.reduction_arity_bits.len()
@@ -303,8 +305,10 @@ impl<F: RichField + Extendable<D>, const D: usize> CompressedFriProof<F, D> {
                 } = query_round_proofs.steps[i][&index].clone();
                 steps_indices[i].push(index);
                 if let Some(v) = evals_by_depth[i].get(&index) {
+                    // If this index has already been seen, get `evals` from the `HashMap`.
                     evals = v.to_vec();
                 } else {
+                    // Otherwise insert the next inferred element.
                     evals.insert(
                         index_within_coset,
                         fri_query_inferred_elements.next().unwrap(),
diff --git a/src/fri/verifier.rs b/src/fri/verifier.rs
index dce20c38..add03a9d 100644
--- a/src/fri/verifier.rs
+++ b/src/fri/verifier.rs
@@ -157,10 +157,6 @@ pub(crate) fn fri_combine_initial<F: RichField + Extendable<D>, const D: usize>(
     let config = &common_data.config;
     assert!(D > 1, "Not implemented for D=1.");
     let degree_log = common_data.degree_bits;
-    // debug_assert_eq!(
-    //     degree_log,
-    //     common_data.config.cap_height + proof.evals_proofs[0].1.siblings.len() - config.rate_bits
-    // );
     let subgroup_x = F::Extension::from_basefield(subgroup_x);
     let mut alpha = ReducingFactor::new(alpha);
     let mut sum = F::Extension::ZERO;
diff --git a/src/plonk/get_challenges.rs b/src/plonk/get_challenges.rs
index c579aa46..0f6888b3 100644
--- a/src/plonk/get_challenges.rs
+++ b/src/plonk/get_challenges.rs
@@ -152,12 +152,15 @@ impl<F: RichField + Extendable<D>, const D: usize> CompressedProofWithPublicInpu
             .map(|_| challenger.get_challenge().to_canonical_u64() as usize % lde_size)
             .collect::<Vec<_>>();
 
+        let mut fri_query_inferred_elements = Vec::new();
+        // Holds the indices that have already been seen at each reduction depth.
         let mut seen_indices_by_depth =
             vec![HashSet::new(); common_data.fri_params.reduction_arity_bits.len()];
         let precomputed_reduced_evals =
             PrecomputedReducedEvals::from_os_and_alpha(&self.proof.openings, fri_alpha);
-        let mut fri_query_inferred_elements = Vec::new();
         let log_n = common_data.degree_bits + common_data.config.rate_bits;
+        // Simulate the proof verification and add collect the inferred elements.
+        // The content of the loop is basically the same as the ` fri_verifier_query_round` function.
         for &(mut x_index) in &fri_query_indices {
             let mut subgroup_x = F::MULTIPLICATIVE_GROUP_GENERATOR
                 * F::primitive_root_of_unity(log_n).exp_u64(reverse_bits(x_index, log_n) as u64);
@@ -180,6 +183,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CompressedProofWithPublicInpu
                 .enumerate()
             {
                 if !seen_indices_by_depth[i].insert(x_index >> arity_bits) {
+                    // If this index has already been seen, we can skip the rest of the reductions.
                     break;
                 }
                 fri_query_inferred_elements.push(old_eval);
diff --git a/src/plonk/proof.rs b/src/plonk/proof.rs
index ecc4e3a4..5a0abfd7 100644
--- a/src/plonk/proof.rs
+++ b/src/plonk/proof.rs
@@ -168,7 +168,6 @@ impl<F: RichField + Extendable<D>, const D: usize> CompressedProofWithPublicInpu
         common_data: &CommonCircuitData<F, D>,
     ) -> anyhow::Result<()> {
         let challenges = self.get_challenges(common_data)?;
-        dbg!(&challenges.fri_query_inferred_elements);
         let compressed_proof = self.proof.decompress(&challenges, common_data);
         verify_with_challenges(
             ProofWithPublicInputs {
@@ -329,18 +328,6 @@ mod tests {
         // Verify that `decompress ∘ compress = identity`.
         let compressed_proof = proof.clone().compress(&data.common)?;
         let decompressed_compressed_proof = compressed_proof.clone().decompress(&data.common)?;
-        for i in 0..proof.proof.opening_proof.query_round_proofs.len() {
-            let qrp = proof.proof.opening_proof.query_round_proofs[i].clone();
-            let dqrp = decompressed_compressed_proof
-                .proof
-                .opening_proof
-                .query_round_proofs[i]
-                .clone();
-            for j in 0..qrp.steps.len() {
-                dbg!(&qrp.steps[j].evals);
-                dbg!(&dqrp.steps[j].evals);
-            }
-        }
         assert_eq!(proof, decompressed_compressed_proof);
 
         verify(proof, &data.verifier_only, &data.common)?;
diff --git a/src/util/serialization.rs b/src/util/serialization.rs
index e9164687..172b4d67 100644
--- a/src/util/serialization.rs
+++ b/src/util/serialization.rs
@@ -242,7 +242,6 @@ impl Buffer {
         &mut self,
         fqs: &FriQueryStep<F, D>,
     ) -> Result<()> {
-        dbg!(self.0.position());
         self.write_field_ext_vec::<F, D>(&fqs.evals)?;
         self.write_merkle_proof(&fqs.merkle_proof)
     }
@@ -251,7 +250,6 @@ impl Buffer {
         arity: usize,
         compressed: bool,
     ) -> Result<FriQueryStep<F, D>> {
-        dbg!(self.0.position());
         let evals = self.read_field_ext_vec::<F, D>(arity - if compressed { 1 } else { 0 })?;
         let merkle_proof = self.read_merkle_proof()?;
         Ok(FriQueryStep {