diff --git a/core/src/utils/config.rs b/core/src/utils/config.rs
index b7939666e4..582ce68c5a 100644
--- a/core/src/utils/config.rs
+++ b/core/src/utils/config.rs
@@ -15,7 +15,7 @@ use p3_symmetric::Hash;
 use p3_symmetric::{PaddingFreeSponge, TruncatedPermutation};
 use serde::Deserialize;
 use serde::Serialize;
-use sp1_primitives::poseidon2_init;
+use sp1_primitives::{poseidon2_16_init, poseidon2_24_init};
 
 pub const DIGEST_SIZE: usize = 8;
 
@@ -24,10 +24,12 @@ pub type InnerVal = BabyBear;
 pub type InnerChallenge = BinomialExtensionField<InnerVal, 4>;
 pub type InnerPerm =
     Poseidon2<InnerVal, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 24, 7>;
+pub type InnerPerm16 =
+    Poseidon2<InnerVal, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 16, 7>;
 pub type InnerHash = PaddingFreeSponge<InnerPerm, 24, 16, 8>;
 pub type InnerDigestHash = Hash<InnerVal, InnerVal, DIGEST_SIZE>;
 pub type InnerDigest = [InnerVal; DIGEST_SIZE];
-pub type InnerCompress = TruncatedPermutation<InnerPerm, 2, 8, 24>;
+pub type InnerCompress = TruncatedPermutation<InnerPerm16, 2, 8, 16>;
 pub type InnerValMmcs = FieldMerkleTreeMmcs<
     <InnerVal as Field>::Packing,
     <InnerVal as Field>::Packing,
@@ -48,14 +50,19 @@ pub type InnerPcsProof =
 
 /// The permutation for inner recursion.
 pub fn inner_perm() -> InnerPerm {
-    poseidon2_init()
+    poseidon2_24_init()
+}
+
+pub fn inner_perm16() -> InnerPerm16 {
+    poseidon2_16_init()
 }
 
 /// The FRI config for sp1 proofs.
 pub fn sp1_fri_config() -> FriConfig<InnerChallengeMmcs> {
     let perm = inner_perm();
+    let perm16 = inner_perm16();
     let hash = InnerHash::new(perm.clone());
-    let compress = InnerCompress::new(perm.clone());
+    let compress = InnerCompress::new(perm16.clone());
     let challenge_mmcs = InnerChallengeMmcs::new(InnerValMmcs::new(hash, compress));
     let num_queries = match std::env::var("FRI_QUERIES") {
         Ok(value) => value.parse().unwrap(),
@@ -72,8 +79,9 @@ pub fn sp1_fri_config() -> FriConfig<InnerChallengeMmcs> {
 /// The FRI config for inner recursion.
 pub fn inner_fri_config() -> FriConfig<InnerChallengeMmcs> {
     let perm = inner_perm();
+    let perm16 = inner_perm16();
     let hash = InnerHash::new(perm.clone());
-    let compress = InnerCompress::new(perm.clone());
+    let compress = InnerCompress::new(perm16.clone());
     let challenge_mmcs = InnerChallengeMmcs::new(InnerValMmcs::new(hash, compress));
     let num_queries = match std::env::var("FRI_QUERIES") {
         Ok(value) => value.parse().unwrap(),
@@ -119,8 +127,9 @@ impl From<std::marker::PhantomData<BabyBearPoseidon2Inner>> for BabyBearPoseidon
 impl BabyBearPoseidon2Inner {
     pub fn new() -> Self {
         let perm = inner_perm();
+        let perm16 = inner_perm16();
         let hash = InnerHash::new(perm.clone());
-        let compress = InnerCompress::new(perm.clone());
+        let compress = InnerCompress::new(perm16.clone());
         let val_mmcs = InnerValMmcs::new(hash, compress);
         let dft = InnerDft {};
         let fri_config = inner_fri_config();
diff --git a/core/src/utils/prove.rs b/core/src/utils/prove.rs
index 25852d6c0e..b7716ca029 100644
--- a/core/src/utils/prove.rs
+++ b/core/src/utils/prove.rs
@@ -403,7 +403,7 @@ pub mod baby_bear_poseidon2 {
     use p3_poseidon2::Poseidon2ExternalMatrixGeneral;
     use p3_symmetric::{PaddingFreeSponge, TruncatedPermutation};
     use serde::{Deserialize, Serialize};
-    use sp1_primitives::RC_24_29;
+    use sp1_primitives::{RC_24_29, RC_16_30};
 
     use crate::stark::StarkGenericConfig;
 
@@ -411,8 +411,9 @@ pub mod baby_bear_poseidon2 {
     pub type Challenge = BinomialExtensionField<Val, 4>;
 
     pub type Perm = Poseidon2<Val, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 24, 7>;
+    pub type Perm16 = Poseidon2<Val, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 16, 7>;
     pub type MyHash = PaddingFreeSponge<Perm, 24, 16, 8>;
-    pub type MyCompress = TruncatedPermutation<Perm, 2, 8, 24>;
+    pub type MyCompress = TruncatedPermutation<Perm16, 2, 8, 16>;
     pub type ValMmcs = FieldMerkleTreeMmcs<
         <Val as Field>::Packing,
         <Val as Field>::Packing,
@@ -445,11 +446,34 @@ pub mod baby_bear_poseidon2 {
             DiffusionMatrixBabyBear,
         )
     }
+    
+    pub fn my_perm16() -> Perm16 {
+        const ROUNDS_F: usize = 8;
+        const ROUNDS_P: usize = 13;
+        let mut round_constants = RC_16_30.to_vec();
+        let internal_start = ROUNDS_F / 2;
+        let internal_end = (ROUNDS_F / 2) + ROUNDS_P;
+        let internal_round_constants = round_constants
+            .drain(internal_start..internal_end)
+            .map(|vec| vec[0])
+            .collect::<Vec<_>>();
+        let external_round_constants = round_constants;
+        Perm16::new(
+            ROUNDS_F,
+            external_round_constants,
+            Poseidon2ExternalMatrixGeneral,
+            ROUNDS_P,
+            internal_round_constants,
+            DiffusionMatrixBabyBear,
+        )
+    }
+
 
     pub fn default_fri_config() -> FriConfig<ChallengeMmcs> {
         let perm = my_perm();
+        let perm16 = my_perm16();
         let hash = MyHash::new(perm.clone());
-        let compress = MyCompress::new(perm.clone());
+        let compress = MyCompress::new(perm16.clone());
         let challenge_mmcs = ChallengeMmcs::new(ValMmcs::new(hash, compress));
         let num_queries = match std::env::var("FRI_QUERIES") {
             Ok(value) => value.parse().unwrap(),
@@ -465,8 +489,9 @@ pub mod baby_bear_poseidon2 {
 
     pub fn compressed_fri_config() -> FriConfig<ChallengeMmcs> {
         let perm = my_perm();
+        let perm16 = my_perm16();
         let hash = MyHash::new(perm.clone());
-        let compress = MyCompress::new(perm.clone());
+        let compress = MyCompress::new(perm16.clone());
         let challenge_mmcs = ChallengeMmcs::new(ValMmcs::new(hash, compress));
         let num_queries = match std::env::var("FRI_QUERIES") {
             Ok(value) => value.parse().unwrap(),
@@ -496,8 +521,9 @@ pub mod baby_bear_poseidon2 {
     impl BabyBearPoseidon2 {
         pub fn new() -> Self {
             let perm = my_perm();
+            let perm16 = my_perm16();
             let hash = MyHash::new(perm.clone());
-            let compress = MyCompress::new(perm.clone());
+            let compress = MyCompress::new(perm16.clone());
             let val_mmcs = ValMmcs::new(hash, compress);
             let dft = Dft {};
             let fri_config = default_fri_config();
@@ -511,8 +537,9 @@ pub mod baby_bear_poseidon2 {
 
         pub fn compressed() -> Self {
             let perm = my_perm();
+            let perm16 = my_perm16();
             let hash = MyHash::new(perm.clone());
-            let compress = MyCompress::new(perm.clone());
+            let compress = MyCompress::new(perm16.clone());
             let val_mmcs = ValMmcs::new(hash, compress);
             let dft = Dft {};
             let fri_config = compressed_fri_config();
diff --git a/primitives/src/lib.rs b/primitives/src/lib.rs
index a5e0996218..0d8a027bc2 100644
--- a/primitives/src/lib.rs
+++ b/primitives/src/lib.rs
@@ -1137,7 +1137,29 @@ lazy_static! {
     };
 }
 
-pub fn poseidon2_init(
+pub fn poseidon2_16_init(
+) -> Poseidon2<BabyBear, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 16, 7> {
+    const ROUNDS_F: usize = 8;
+    const ROUNDS_P: usize = 13;
+    let mut round_constants = RC_16_30.to_vec();
+    let internal_start = ROUNDS_F / 2;
+    let internal_end = (ROUNDS_F / 2) + ROUNDS_P;
+    let internal_round_constants = round_constants
+        .drain(internal_start..internal_end)
+        .map(|vec| vec[0])
+        .collect::<Vec<_>>();
+    let external_round_constants = round_constants;
+    Poseidon2::new(
+        ROUNDS_F,
+        external_round_constants,
+        Poseidon2ExternalMatrixGeneral,
+        ROUNDS_P,
+        internal_round_constants,
+        DiffusionMatrixBabyBear,
+    )
+}
+
+pub fn poseidon2_24_init(
 ) -> Poseidon2<BabyBear, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 24, 7> {
     const ROUNDS_F: usize = 8;
     const ROUNDS_P: usize = 21;
@@ -1166,7 +1188,7 @@ mod tests {
 
     #[test]
     fn test_24_permutation() {
-        let h1 = poseidon2_init();
+        let h1 = poseidon2_24_init();
 
         type Perm = Poseidon2<BabyBear, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 24, 7>;
         let h2 = Perm::new_from_rng_128(
@@ -1209,7 +1231,7 @@ pub fn poseidon2_hasher() -> PaddingFreeSponge<
     16,
     8,
 > {
-    let hasher = poseidon2_init();
+    let hasher = poseidon2_24_init();
     PaddingFreeSponge::<
         Poseidon2<BabyBear, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 24, 7>,
         24,
diff --git a/recursion/program/src/fri/two_adic_pcs.rs b/recursion/program/src/fri/two_adic_pcs.rs
index 71b361f8ef..936baa9767 100644
--- a/recursion/program/src/fri/two_adic_pcs.rs
+++ b/recursion/program/src/fri/two_adic_pcs.rs
@@ -282,6 +282,7 @@ pub mod tests {
     use rand::rngs::OsRng;
     use sp1_core::utils::baby_bear_poseidon2::compressed_fri_config;
     use sp1_core::utils::inner_perm;
+    use sp1_core::utils::inner_perm16;
     use sp1_core::utils::InnerChallenge;
     use sp1_core::utils::InnerChallenger;
     use sp1_core::utils::InnerCompress;
@@ -307,9 +308,10 @@ pub mod tests {
         let mut rng = &mut OsRng;
         let log_degrees = &[nb_log2_rows];
         let perm = inner_perm();
+        let perm16 = inner_perm16();
         let fri_config = compressed_fri_config();
         let hash = InnerHash::new(perm.clone());
-        let compress = InnerCompress::new(perm.clone());
+        let compress = InnerCompress::new(perm16.clone());
         let val_mmcs = InnerValMmcs::new(hash, compress);
         let dft = InnerDft {};
         let pcs_val: InnerPcs = InnerPcs::new(
diff --git a/recursion/program/src/utils.rs b/recursion/program/src/utils.rs
index 83b7b2adbe..ae4cd98c1e 100644
--- a/recursion/program/src/utils.rs
+++ b/recursion/program/src/utils.rs
@@ -27,8 +27,9 @@ type C = AsmConfig<F, EF>;
 type Val = BabyBear;
 type Challenge = BinomialExtensionField<Val, 4>;
 type Perm = Poseidon2<Val, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 24, 7>;
+type Perm16 = Poseidon2<Val, Poseidon2ExternalMatrixGeneral, DiffusionMatrixBabyBear, 16, 7>;
 type Hash = PaddingFreeSponge<Perm, 24, 16, 8>;
-type Compress = TruncatedPermutation<Perm, 2, 8, 24>;
+type Compress = TruncatedPermutation<Perm16, 2, 8, 16>;
 type ValMmcs =
     FieldMerkleTreeMmcs<<Val as Field>::Packing, <Val as Field>::Packing, Hash, Compress, 8>;
 type ChallengeMmcs = ExtensionMmcs<Val, Challenge, ValMmcs>;