diff --git a/Cargo.toml b/Cargo.toml
index 67610c780..153cf07a2 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -121,6 +121,9 @@ lto = "fat"
 codegen-units = 1
 panic = "abort"
 
+[profile.dev.package."libcrux-ml-dsa"]
+opt-level = 1
+
 [lints.rust]
 unexpected_cfgs = { level = "warn", check-cfg = [
     'cfg(hax)',
diff --git a/libcrux-ml-dsa/src/ml_dsa_generic.rs b/libcrux-ml-dsa/src/ml_dsa_generic.rs
index 9b0443525..987f99621 100644
--- a/libcrux-ml-dsa/src/ml_dsa_generic.rs
+++ b/libcrux-ml-dsa/src/ml_dsa_generic.rs
@@ -52,9 +52,8 @@ pub(crate) fn generate_key_pair<
     let (seed_for_error_vectors, seed_for_signing) =
         seed_expanded.split_at(SEED_FOR_ERROR_VECTORS_SIZE);
 
-    let a_as_ntt = samplex4::matrix_A::<SIMDUnit, Shake128X4, ROWS_IN_A, COLUMNS_IN_A>(
-        into_padded_array(seed_for_a),
-    );
+    let a_as_ntt =
+        samplex4::matrix_A::<SIMDUnit, ROWS_IN_A, COLUMNS_IN_A>(into_padded_array(seed_for_a));
 
     let (s1, s2) = samplex4::sample_s1_and_s2::<SIMDUnit, Shake256X4, ETA, COLUMNS_IN_A, ROWS_IN_A>(
         into_padded_array(seed_for_error_vectors),
@@ -246,9 +245,8 @@ pub(crate) fn sign_internal<
             SIGNING_KEY_SIZE,
         >(signing_key);
 
-    let A_as_ntt = samplex4::matrix_A::<SIMDUnit, Shake128X4, ROWS_IN_A, COLUMNS_IN_A>(
-        into_padded_array(&seed_for_A),
-    );
+    let A_as_ntt =
+        samplex4::matrix_A::<SIMDUnit, ROWS_IN_A, COLUMNS_IN_A>(into_padded_array(&seed_for_A));
 
     let mut message_representative = [0; MESSAGE_REPRESENTATIVE_SIZE];
     derive_message_representative(
@@ -492,9 +490,8 @@ pub(crate) fn verify_internal<
         signature.signer_response,
         (2 << GAMMA1_EXPONENT) - BETA,
     ) {
-        let A_as_ntt = samplex4::matrix_A::<SIMDUnit, Shake128X4, ROWS_IN_A, COLUMNS_IN_A>(
-            into_padded_array(&seed_for_A),
-        );
+        let A_as_ntt =
+            samplex4::matrix_A::<SIMDUnit, ROWS_IN_A, COLUMNS_IN_A>(into_padded_array(&seed_for_A));
 
         let mut verification_key_hash = [0; BYTES_FOR_VERIFICATION_KEY_HASH];
         Shake256::shake256::<BYTES_FOR_VERIFICATION_KEY_HASH>(
diff --git a/libcrux-ml-dsa/src/sample.rs b/libcrux-ml-dsa/src/sample.rs
index 99e7d33f2..16f2b1f65 100644
--- a/libcrux-ml-dsa/src/sample.rs
+++ b/libcrux-ml-dsa/src/sample.rs
@@ -31,8 +31,7 @@ fn rejection_sample_less_than_field_modulus<SIMDUnit: Operations>(
     done
 }
 
-#[inline(always)]
-pub(crate) fn sample_four_ring_elements<SIMDUnit: Operations, Shake128: shake128::XofX4>(
+pub(crate) fn sample_four_ring_elements<SIMDUnit: Operations>(
     mut seed0: [u8; 34],
     domain_separator0: u16,
     domain_separator1: u16,
@@ -44,6 +43,8 @@ pub(crate) fn sample_four_ring_elements<SIMDUnit: Operations, Shake128: shake128
     PolynomialRingElement<SIMDUnit>,
     PolynomialRingElement<SIMDUnit>,
 ) {
+    use crate::hash_functions::shake128::XofX4;
+
     // Prepare the seeds
     seed0[32] = domain_separator0 as u8;
     seed0[33] = (domain_separator0 >> 8) as u8;
@@ -60,7 +61,12 @@ pub(crate) fn sample_four_ring_elements<SIMDUnit: Operations, Shake128: shake128
     seed3[32] = domain_separator3 as u8;
     seed3[33] = (domain_separator3 >> 8) as u8;
 
-    let mut state = Shake128::init_absorb(&seed0, &seed1, &seed2, &seed3);
+    // FIXME: We use the portable implementation here, since the
+    // compiler has an easier time optimizing it, compared to the AVX2
+    // version, which actually results in faster code (except for key
+    // generation), even in the AVX2 instantiation of ML-DSA.
+    let mut state =
+        crate::hash_functions::portable::Shake128X4::init_absorb(&seed0, &seed1, &seed2, &seed3);
 
     let mut randomness0 = [0u8; shake128::FIVE_BLOCKS_SIZE];
     let mut randomness1 = [0u8; shake128::FIVE_BLOCKS_SIZE];
@@ -483,10 +489,10 @@ mod tests {
 
     // This is just a wrapper around sample_four_ring_elements, for testing
     // purposes.
-    fn sample_ring_element_uniform<SIMDUnit: Operations, Shake128: shake128::XofX4>(
+    fn sample_ring_element_uniform<SIMDUnit: Operations>(
         seed: [u8; 34],
     ) -> PolynomialRingElement<SIMDUnit> {
-        let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128>(
+        let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
             seed,
             ((seed[33] as u16) << 8) | (seed[32] as u16),
             0,
@@ -554,7 +560,7 @@ mod tests {
         ];
 
         assert_eq!(
-            sample_ring_element_uniform::<SIMDUnit, Shake128>(seed).to_i32_array(),
+            sample_ring_element_uniform::<SIMDUnit>(seed).to_i32_array(),
             expected_coefficients
         );
 
@@ -568,8 +574,7 @@ mod tests {
             0xB1, 0x83, 0x9B, 0x86, 0x06, 0xF5, 0x94, 0x8B, 0x9D, 0x72, 0xA9, 0x56, 0xDC, 0xF1,
             0x01, 0x16, 0xDA, 0x9E, 0x01, 0x00,
         ];
-        let actual_coefficients =
-            sample_ring_element_uniform::<SIMDUnit, Shake128>(seed).to_i32_array();
+        let actual_coefficients = sample_ring_element_uniform::<SIMDUnit>(seed).to_i32_array();
 
         assert_eq!(actual_coefficients[0], 1_165_602);
         assert_eq!(
diff --git a/libcrux-ml-dsa/src/samplex4.rs b/libcrux-ml-dsa/src/samplex4.rs
index 918deb8ce..1ac7e7530 100644
--- a/libcrux-ml-dsa/src/samplex4.rs
+++ b/libcrux-ml-dsa/src/samplex4.rs
@@ -1,5 +1,5 @@
 use crate::{
-    hash_functions::{shake128, shake256},
+    hash_functions::shake256,
     polynomial::PolynomialRingElement,
     sample::{sample_four_error_ring_elements, sample_four_ring_elements},
     simd::traits::Operations,
@@ -30,7 +30,6 @@ fn update_matrix<SIMDUnit: Operations, const ROWS_IN_A: usize, const COLUMNS_IN_
 #[inline(always)]
 pub(crate) fn matrix_A_4_by_4<
     SIMDUnit: Operations,
-    Shake128X4: shake128::XofX4,
     const ROWS_IN_A: usize,
     const COLUMNS_IN_A: usize,
 >(
@@ -39,7 +38,7 @@ pub(crate) fn matrix_A_4_by_4<
     let mut A: Matrix<SIMDUnit, ROWS_IN_A, COLUMNS_IN_A> =
         [[PolynomialRingElement::<SIMDUnit>::ZERO(); COLUMNS_IN_A]; ROWS_IN_A];
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(0, 0),
         generate_domain_separator(0, 1),
@@ -51,7 +50,7 @@ pub(crate) fn matrix_A_4_by_4<
     update_matrix(&mut A, 0, 2, four_ring_elements.2);
     update_matrix(&mut A, 0, 3, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(1, 0),
         generate_domain_separator(1, 1),
@@ -63,7 +62,7 @@ pub(crate) fn matrix_A_4_by_4<
     update_matrix(&mut A, 1, 2, four_ring_elements.2);
     update_matrix(&mut A, 1, 3, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(2, 0),
         generate_domain_separator(2, 1),
@@ -75,7 +74,7 @@ pub(crate) fn matrix_A_4_by_4<
     update_matrix(&mut A, 2, 2, four_ring_elements.2);
     update_matrix(&mut A, 2, 3, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(3, 0),
         generate_domain_separator(3, 1),
@@ -94,7 +93,6 @@ pub(crate) fn matrix_A_4_by_4<
 #[inline(always)]
 pub(crate) fn matrix_A_6_by_5<
     SIMDUnit: Operations,
-    Shake128X4: shake128::XofX4,
     const ROWS_IN_A: usize,
     const COLUMNS_IN_A: usize,
 >(
@@ -102,7 +100,7 @@ pub(crate) fn matrix_A_6_by_5<
 ) -> [[PolynomialRingElement<SIMDUnit>; COLUMNS_IN_A]; ROWS_IN_A] {
     let mut A = [[PolynomialRingElement::<SIMDUnit>::ZERO(); COLUMNS_IN_A]; ROWS_IN_A];
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(0, 0),
         generate_domain_separator(0, 1),
@@ -114,7 +112,7 @@ pub(crate) fn matrix_A_6_by_5<
     update_matrix(&mut A, 0, 2, four_ring_elements.2);
     update_matrix(&mut A, 0, 3, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(0, 4),
         generate_domain_separator(1, 0),
@@ -126,7 +124,7 @@ pub(crate) fn matrix_A_6_by_5<
     update_matrix(&mut A, 1, 1, four_ring_elements.2);
     update_matrix(&mut A, 1, 2, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(1, 3),
         generate_domain_separator(1, 4),
@@ -138,7 +136,7 @@ pub(crate) fn matrix_A_6_by_5<
     update_matrix(&mut A, 2, 0, four_ring_elements.2);
     update_matrix(&mut A, 2, 1, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(2, 2),
         generate_domain_separator(2, 3),
@@ -150,7 +148,7 @@ pub(crate) fn matrix_A_6_by_5<
     update_matrix(&mut A, 2, 4, four_ring_elements.2);
     update_matrix(&mut A, 3, 0, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(3, 1),
         generate_domain_separator(3, 2),
@@ -162,7 +160,7 @@ pub(crate) fn matrix_A_6_by_5<
     update_matrix(&mut A, 3, 3, four_ring_elements.2);
     update_matrix(&mut A, 3, 4, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(4, 0),
         generate_domain_separator(4, 1),
@@ -174,7 +172,7 @@ pub(crate) fn matrix_A_6_by_5<
     update_matrix(&mut A, 4, 2, four_ring_elements.2);
     update_matrix(&mut A, 4, 3, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(4, 4),
         generate_domain_separator(5, 0),
@@ -187,7 +185,7 @@ pub(crate) fn matrix_A_6_by_5<
     update_matrix(&mut A, 5, 2, four_ring_elements.3);
 
     // The the last 2 sampled ring elements are discarded here.
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(5, 3),
         generate_domain_separator(5, 4),
@@ -203,7 +201,6 @@ pub(crate) fn matrix_A_6_by_5<
 #[inline(always)]
 pub(crate) fn matrix_A_8_by_7<
     SIMDUnit: Operations,
-    Shake128X4: shake128::XofX4,
     const ROWS_IN_A: usize,
     const COLUMNS_IN_A: usize,
 >(
@@ -211,7 +208,7 @@ pub(crate) fn matrix_A_8_by_7<
 ) -> [[PolynomialRingElement<SIMDUnit>; COLUMNS_IN_A]; ROWS_IN_A] {
     let mut A = [[PolynomialRingElement::<SIMDUnit>::ZERO(); COLUMNS_IN_A]; ROWS_IN_A];
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(0, 0),
         generate_domain_separator(0, 1),
@@ -223,7 +220,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 0, 2, four_ring_elements.2);
     update_matrix(&mut A, 0, 3, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(0, 4),
         generate_domain_separator(0, 5),
@@ -235,7 +232,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 0, 6, four_ring_elements.2);
     update_matrix(&mut A, 1, 0, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(1, 1),
         generate_domain_separator(1, 2),
@@ -247,7 +244,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 1, 3, four_ring_elements.2);
     update_matrix(&mut A, 1, 4, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(1, 5),
         generate_domain_separator(1, 6),
@@ -259,7 +256,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 2, 0, four_ring_elements.2);
     update_matrix(&mut A, 2, 1, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(2, 2),
         generate_domain_separator(2, 3),
@@ -271,7 +268,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 2, 4, four_ring_elements.2);
     update_matrix(&mut A, 2, 5, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(2, 6),
         generate_domain_separator(3, 0),
@@ -283,7 +280,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 3, 1, four_ring_elements.2);
     update_matrix(&mut A, 3, 2, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(3, 3),
         generate_domain_separator(3, 4),
@@ -295,7 +292,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 3, 5, four_ring_elements.2);
     update_matrix(&mut A, 3, 6, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(4, 0),
         generate_domain_separator(4, 1),
@@ -307,7 +304,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 4, 2, four_ring_elements.2);
     update_matrix(&mut A, 4, 3, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(4, 4),
         generate_domain_separator(4, 5),
@@ -319,7 +316,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 4, 6, four_ring_elements.2);
     update_matrix(&mut A, 5, 0, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(5, 1),
         generate_domain_separator(5, 2),
@@ -331,7 +328,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 5, 3, four_ring_elements.2);
     update_matrix(&mut A, 5, 4, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(5, 5),
         generate_domain_separator(5, 6),
@@ -343,7 +340,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 6, 0, four_ring_elements.2);
     update_matrix(&mut A, 6, 1, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(6, 2),
         generate_domain_separator(6, 3),
@@ -355,7 +352,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 6, 4, four_ring_elements.2);
     update_matrix(&mut A, 6, 5, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(6, 6),
         generate_domain_separator(7, 0),
@@ -367,7 +364,7 @@ pub(crate) fn matrix_A_8_by_7<
     update_matrix(&mut A, 7, 1, four_ring_elements.2);
     update_matrix(&mut A, 7, 2, four_ring_elements.3);
 
-    let four_ring_elements = sample_four_ring_elements::<SIMDUnit, Shake128X4>(
+    let four_ring_elements = sample_four_ring_elements::<SIMDUnit>(
         seed,
         generate_domain_separator(7, 3),
         generate_domain_separator(7, 4),
@@ -383,18 +380,13 @@ pub(crate) fn matrix_A_8_by_7<
 }
 #[allow(non_snake_case)]
 #[inline(always)]
-pub(crate) fn matrix_A<
-    SIMDUnit: Operations,
-    Shake128X4: shake128::XofX4,
-    const ROWS_IN_A: usize,
-    const COLUMNS_IN_A: usize,
->(
+pub(crate) fn matrix_A<SIMDUnit: Operations, const ROWS_IN_A: usize, const COLUMNS_IN_A: usize>(
     seed: [u8; 34],
 ) -> [[PolynomialRingElement<SIMDUnit>; COLUMNS_IN_A]; ROWS_IN_A] {
     match (ROWS_IN_A as u8, COLUMNS_IN_A as u8) {
-        (4, 4) => matrix_A_4_by_4::<SIMDUnit, Shake128X4, ROWS_IN_A, COLUMNS_IN_A>(seed),
-        (6, 5) => matrix_A_6_by_5::<SIMDUnit, Shake128X4, ROWS_IN_A, COLUMNS_IN_A>(seed),
-        (8, 7) => matrix_A_8_by_7::<SIMDUnit, Shake128X4, ROWS_IN_A, COLUMNS_IN_A>(seed),
+        (4, 4) => matrix_A_4_by_4::<SIMDUnit, ROWS_IN_A, COLUMNS_IN_A>(seed),
+        (6, 5) => matrix_A_6_by_5::<SIMDUnit, ROWS_IN_A, COLUMNS_IN_A>(seed),
+        (8, 7) => matrix_A_8_by_7::<SIMDUnit, ROWS_IN_A, COLUMNS_IN_A>(seed),
         _ => unreachable!(),
     }
 }