diff --git a/src/bin/bench_recursion.rs b/src/bin/bench_recursion.rs
index 12af72df..efab1dd8 100644
--- a/src/bin/bench_recursion.rs
+++ b/src/bin/bench_recursion.rs
@@ -9,7 +9,6 @@ use plonky2::fri::FriConfig;
 use plonky2::gates::constant::ConstantGate;
 use plonky2::gates::gmimc::GMiMCGate;
 use plonky2::hash::GMIMC_ROUNDS;
-use plonky2::polynomial::commitment::EXTENSION_DEGREE;
 use plonky2::prover::PLONK_BLINDING;
 use plonky2::witness::PartialWitness;
 
diff --git a/src/circuit_data.rs b/src/circuit_data.rs
index cae1501f..d45192cb 100644
--- a/src/circuit_data.rs
+++ b/src/circuit_data.rs
@@ -4,7 +4,7 @@ use crate::fri::FriConfig;
 use crate::gates::gate::GateRef;
 use crate::generator::WitnessGenerator;
 use crate::merkle_tree::MerkleTree;
-use crate::polynomial::commitment::{ListPolynomialCommitment, EXTENSION_DEGREE};
+use crate::polynomial::commitment::ListPolynomialCommitment;
 use crate::proof::{Hash, HashTarget, Proof};
 use crate::prover::prove;
 use crate::verifier::verify;
diff --git a/src/fri/mod.rs b/src/fri/mod.rs
index a81fda1e..480980ca 100644
--- a/src/fri/mod.rs
+++ b/src/fri/mod.rs
@@ -54,29 +54,25 @@ mod tests {
     use crate::field::crandall_field::CrandallField;
     use crate::field::extension_field::quadratic::QuadraticCrandallField;
     use crate::field::extension_field::quartic::QuarticCrandallField;
-    use crate::field::extension_field::{flatten, FieldExtension};
+    use crate::field::extension_field::{flatten, Extendable, FieldExtension};
     use crate::field::fft::ifft;
     use crate::field::field::Field;
     use crate::fri::prover::fri_proof;
     use crate::fri::verifier::verify_fri_proof;
     use crate::merkle_tree::MerkleTree;
     use crate::plonk_challenger::Challenger;
-    use crate::polynomial::commitment::EXTENSION_DEGREE;
     use crate::polynomial::polynomial::{PolynomialCoeffs, PolynomialValues};
     use crate::util::reverse_index_bits_in_place;
     use anyhow::Result;
     use rand::rngs::ThreadRng;
     use rand::Rng;
 
-    fn test_fri(
+    fn check_fri<F: Field + Extendable<D>, const D: usize>(
         degree_log: usize,
         rate_bits: usize,
         reduction_arity_bits: Vec<usize>,
         num_query_rounds: usize,
     ) -> Result<()> {
-        type F = CrandallField;
-        type F2 = QuadraticCrandallField;
-
         let n = 1 << degree_log;
         let coeffs = PolynomialCoeffs::new(F::rand_vec(n)).lde(rate_bits);
         let coset_lde = coeffs.clone().coset_fft(F::MULTIPLICATIVE_GROUP_GENERATOR);
@@ -96,13 +92,18 @@ mod tests {
             reverse_index_bits_in_place(&mut leaves);
             MerkleTree::new(leaves, false)
         };
-        let coset_lde =
-            PolynomialValues::new(coset_lde.values.into_iter().map(|x| F2::from(x)).collect());
+        let coset_lde = PolynomialValues::new(
+            coset_lde
+                .values
+                .into_iter()
+                .map(|x| F::Extension::from(x))
+                .collect(),
+        );
         let root = tree.root;
         let mut challenger = Challenger::new();
-        let proof = fri_proof::<F, 2>(
+        let proof = fri_proof::<F, D>(
             &[&tree],
-            &coeffs.to_extension::<2>(),
+            &coeffs.to_extension::<D>(),
             &coset_lde,
             &mut challenger,
             &config,
@@ -112,7 +113,7 @@ mod tests {
         verify_fri_proof(
             degree_log,
             &[],
-            F2::ONE,
+            F::Extension::ONE,
             &[root],
             &proof,
             &mut challenger,
@@ -133,14 +134,13 @@ mod tests {
         arities
     }
 
-    #[test]
-    fn test_fri_multi_params() -> Result<()> {
+    fn check_fri_multi_params<F: Field + Extendable<D>, const D: usize>() -> Result<()> {
         let mut rng = rand::thread_rng();
         for degree_log in 1..6 {
             for rate_bits in 0..3 {
                 for num_query_round in 0..4 {
                     for _ in 0..3 {
-                        test_fri(
+                        check_fri::<F, D>(
                             degree_log,
                             rate_bits,
                             gen_arities(degree_log, &mut rng),
@@ -152,4 +152,37 @@ mod tests {
         }
         Ok(())
     }
+
+    mod base {
+        use super::*;
+        type F = CrandallField;
+        const D: usize = 1;
+
+        #[test]
+        fn test_fri_multi_params() -> Result<()> {
+            check_fri_multi_params::<F, D>()
+        }
+    }
+
+    mod quadratic {
+        use super::*;
+        type F = CrandallField;
+        const D: usize = 2;
+
+        #[test]
+        fn test_fri_multi_params() -> Result<()> {
+            check_fri_multi_params::<F, D>()
+        }
+    }
+
+    mod quartic {
+        use super::*;
+        type F = CrandallField;
+        const D: usize = 4;
+
+        #[test]
+        fn test_fri_multi_params() -> Result<()> {
+            check_fri_multi_params::<F, D>()
+        }
+    }
 }
diff --git a/src/fri/prover.rs b/src/fri/prover.rs
index 21e24296..cd95c4a6 100644
--- a/src/fri/prover.rs
+++ b/src/fri/prover.rs
@@ -5,7 +5,6 @@ use crate::hash::hash_n_to_1;
 use crate::merkle_tree::MerkleTree;
 use crate::plonk_challenger::Challenger;
 use crate::plonk_common::reduce_with_powers;
-use crate::polynomial::commitment::EXTENSION_DEGREE;
 use crate::polynomial::polynomial::{PolynomialCoeffs, PolynomialValues};
 use crate::proof::{FriInitialTreeProof, FriProof, FriQueryRound, FriQueryStep, Hash};
 use crate::util::reverse_index_bits_in_place;
@@ -136,7 +135,6 @@ fn fri_prover_query_round<F: Field + Extendable<D>, const D: usize>(
     let mut query_steps = Vec::new();
     let x = challenger.get_challenge();
     let mut x_index = x.to_canonical_u64() as usize % n;
-    dbg!(x_index, n);
     let initial_proof = initial_merkle_trees
         .iter()
         .map(|t| (t.get(x_index).to_vec(), t.prove(x_index)))
diff --git a/src/fri/verifier.rs b/src/fri/verifier.rs
index ed090ed3..351f119c 100644
--- a/src/fri/verifier.rs
+++ b/src/fri/verifier.rs
@@ -5,7 +5,7 @@ use crate::fri::FriConfig;
 use crate::hash::hash_n_to_1;
 use crate::merkle_proofs::verify_merkle_proof;
 use crate::plonk_challenger::Challenger;
-use crate::polynomial::commitment::{EXTENSION_DEGREE, SALT_SIZE};
+use crate::polynomial::commitment::SALT_SIZE;
 use crate::polynomial::polynomial::PolynomialCoeffs;
 use crate::proof::{FriInitialTreeProof, FriProof, FriQueryRound, Hash};
 use crate::util::{log2_strict, reverse_bits, reverse_index_bits_in_place};
@@ -35,7 +35,6 @@ fn compute_evaluation<F: Field + Extendable<D>, const D: usize>(
         .zip(evals)
         .map(|(y, e)| ((x * y).into(), e))
         .collect::<Vec<_>>();
-    dbg!(&points);
     let barycentric_weights = barycentric_weights(&points);
     interpolate(&points, beta, &barycentric_weights)
 }
diff --git a/src/polynomial/commitment.rs b/src/polynomial/commitment.rs
index 8a386d6a..48b63eff 100644
--- a/src/polynomial/commitment.rs
+++ b/src/polynomial/commitment.rs
@@ -381,10 +381,7 @@ mod tests {
         (polys, points)
     }
 
-    #[test]
-    fn test_polynomial_commitment() -> Result<()> {
-        type F = CrandallField;
-
+    fn check_polynomial_commitment<F: Field + Extendable<D>, const D: usize>() -> Result<()> {
         let k = 10;
         let degree_log = 11;
         let num_points = 3;
@@ -395,10 +392,10 @@ mod tests {
             num_query_rounds: 3,
             blinding: vec![false],
         };
-        let (polys, points) = gen_random_test_case::<F, 2>(k, degree_log, num_points);
+        let (polys, points) = gen_random_test_case::<F, D>(k, degree_log, num_points);
 
         let lpc = ListPolynomialCommitment::new(polys, fri_config.rate_bits, false);
-        let (proof, evaluations) = lpc.open::<2>(&points, &mut Challenger::new(), &fri_config);
+        let (proof, evaluations) = lpc.open::<D>(&points, &mut Challenger::new(), &fri_config);
         proof.verify(
             &points,
             &evaluations.into_iter().map(|e| vec![e]).collect::<Vec<_>>(),
@@ -408,10 +405,8 @@ mod tests {
         )
     }
 
-    #[test]
-    fn test_polynomial_commitment_blinding() -> Result<()> {
-        type F = CrandallField;
-
+    fn check_polynomial_commitment_blinding<F: Field + Extendable<D>, const D: usize>() -> Result<()>
+    {
         let k = 10;
         let degree_log = 11;
         let num_points = 3;
@@ -422,10 +417,10 @@ mod tests {
             num_query_rounds: 3,
             blinding: vec![true],
         };
-        let (polys, points) = gen_random_test_case::<F, 2>(k, degree_log, num_points);
+        let (polys, points) = gen_random_test_case::<F, D>(k, degree_log, num_points);
 
         let lpc = ListPolynomialCommitment::new(polys, fri_config.rate_bits, true);
-        let (proof, evaluations) = lpc.open::<2>(&points, &mut Challenger::new(), &fri_config);
+        let (proof, evaluations) = lpc.open::<D>(&points, &mut Challenger::new(), &fri_config);
         proof.verify(
             &points,
             &evaluations.into_iter().map(|e| vec![e]).collect::<Vec<_>>(),
@@ -435,10 +430,7 @@ mod tests {
         )
     }
 
-    #[test]
-    fn test_batch_polynomial_commitment() -> Result<()> {
-        type F = CrandallField;
-
+    fn check_batch_polynomial_commitment<F: Field + Extendable<D>, const D: usize>() -> Result<()> {
         let k0 = 10;
         let k1 = 3;
         let k2 = 7;
@@ -451,15 +443,15 @@ mod tests {
             num_query_rounds: 3,
             blinding: vec![false, false, false],
         };
-        let (polys0, _) = gen_random_test_case::<F, 2>(k0, degree_log, num_points);
-        let (polys1, _) = gen_random_test_case::<F, 2>(k0, degree_log, num_points);
-        let (polys2, points) = gen_random_test_case::<F, 2>(k0, degree_log, num_points);
+        let (polys0, _) = gen_random_test_case::<F, D>(k0, degree_log, num_points);
+        let (polys1, _) = gen_random_test_case::<F, D>(k1, degree_log, num_points);
+        let (polys2, points) = gen_random_test_case::<F, D>(k2, degree_log, num_points);
 
         let lpc0 = ListPolynomialCommitment::new(polys0, fri_config.rate_bits, false);
         let lpc1 = ListPolynomialCommitment::new(polys1, fri_config.rate_bits, false);
         let lpc2 = ListPolynomialCommitment::new(polys2, fri_config.rate_bits, false);
 
-        let (proof, evaluations) = ListPolynomialCommitment::batch_open::<2>(
+        let (proof, evaluations) = ListPolynomialCommitment::batch_open::<D>(
             &[&lpc0, &lpc1, &lpc2],
             &points,
             &mut Challenger::new(),
@@ -478,10 +470,8 @@ mod tests {
         )
     }
 
-    #[test]
-    fn test_batch_polynomial_commitment_blinding() -> Result<()> {
-        type F = CrandallField;
-
+    fn check_batch_polynomial_commitment_blinding<F: Field + Extendable<D>, const D: usize>(
+    ) -> Result<()> {
         let k0 = 10;
         let k1 = 3;
         let k2 = 7;
@@ -494,15 +484,15 @@ mod tests {
             num_query_rounds: 3,
             blinding: vec![true, false, true],
         };
-        let (polys0, _) = gen_random_test_case::<F, 2>(k0, degree_log, num_points);
-        let (polys1, _) = gen_random_test_case::<F, 2>(k0, degree_log, num_points);
-        let (polys2, points) = gen_random_test_case::<F, 2>(k0, degree_log, num_points);
+        let (polys0, _) = gen_random_test_case::<F, D>(k0, degree_log, num_points);
+        let (polys1, _) = gen_random_test_case::<F, D>(k1, degree_log, num_points);
+        let (polys2, points) = gen_random_test_case::<F, D>(k2, degree_log, num_points);
 
         let lpc0 = ListPolynomialCommitment::new(polys0, fri_config.rate_bits, true);
         let lpc1 = ListPolynomialCommitment::new(polys1, fri_config.rate_bits, false);
         let lpc2 = ListPolynomialCommitment::new(polys2, fri_config.rate_bits, true);
 
-        let (proof, evaluations) = ListPolynomialCommitment::batch_open::<2>(
+        let (proof, evaluations) = ListPolynomialCommitment::batch_open::<D>(
             &[&lpc0, &lpc1, &lpc2],
             &points,
             &mut Challenger::new(),
@@ -520,4 +510,82 @@ mod tests {
             &fri_config,
         )
     }
+
+    mod base {
+        use super::*;
+        type F = CrandallField;
+        const D: usize = 1;
+
+        #[test]
+        fn test_polynomial_commitment() -> Result<()> {
+            check_polynomial_commitment::<F, D>()
+        }
+
+        #[test]
+        fn test_polynomial_commitment_blinding() -> Result<()> {
+            check_polynomial_commitment_blinding::<F, D>()
+        }
+
+        #[test]
+        fn test_batch_polynomial_commitment() -> Result<()> {
+            check_batch_polynomial_commitment::<F, D>()
+        }
+
+        #[test]
+        fn test_batch_polynomial_commitment_blinding() -> Result<()> {
+            check_batch_polynomial_commitment_blinding::<F, D>()
+        }
+    }
+
+    mod quadratic {
+        use super::*;
+        type F = CrandallField;
+        const D: usize = 2;
+
+        #[test]
+        fn test_polynomial_commitment() -> Result<()> {
+            check_polynomial_commitment::<F, D>()
+        }
+
+        #[test]
+        fn test_polynomial_commitment_blinding() -> Result<()> {
+            check_polynomial_commitment_blinding::<F, D>()
+        }
+
+        #[test]
+        fn test_batch_polynomial_commitment() -> Result<()> {
+            check_batch_polynomial_commitment::<F, D>()
+        }
+
+        #[test]
+        fn test_batch_polynomial_commitment_blinding() -> Result<()> {
+            check_batch_polynomial_commitment_blinding::<F, D>()
+        }
+    }
+
+    mod quartic {
+        use super::*;
+        type F = CrandallField;
+        const D: usize = 4;
+
+        #[test]
+        fn test_polynomial_commitment() -> Result<()> {
+            check_polynomial_commitment::<F, D>()
+        }
+
+        #[test]
+        fn test_polynomial_commitment_blinding() -> Result<()> {
+            check_polynomial_commitment_blinding::<F, D>()
+        }
+
+        #[test]
+        fn test_batch_polynomial_commitment() -> Result<()> {
+            check_batch_polynomial_commitment::<F, D>()
+        }
+
+        #[test]
+        fn test_batch_polynomial_commitment_blinding() -> Result<()> {
+            check_batch_polynomial_commitment_blinding::<F, D>()
+        }
+    }
 }
diff --git a/src/proof.rs b/src/proof.rs
index 03e78f16..b12c24ec 100644
--- a/src/proof.rs
+++ b/src/proof.rs
@@ -1,7 +1,7 @@
 use crate::field::extension_field::Extendable;
 use crate::field::field::Field;
 use crate::merkle_proofs::{MerkleProof, MerkleProofTarget};
-use crate::polynomial::commitment::{ListPolynomialCommitment, OpeningProof, EXTENSION_DEGREE};
+use crate::polynomial::commitment::{ListPolynomialCommitment, OpeningProof};
 use crate::polynomial::polynomial::PolynomialCoeffs;
 use crate::target::Target;
 use std::convert::TryInto;
diff --git a/src/prover.rs b/src/prover.rs
index f9847af5..4a570598 100644
--- a/src/prover.rs
+++ b/src/prover.rs
@@ -10,7 +10,7 @@ use crate::field::field::Field;
 use crate::generator::generate_partial_witness;
 use crate::plonk_challenger::Challenger;
 use crate::plonk_common::{eval_l_1, evaluate_gate_constraints, reduce_with_powers_multi};
-use crate::polynomial::commitment::{ListPolynomialCommitment, EXTENSION_DEGREE};
+use crate::polynomial::commitment::ListPolynomialCommitment;
 use crate::polynomial::polynomial::{PolynomialCoeffs, PolynomialValues};
 use crate::proof::Proof;
 use crate::timed;