diff --git a/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/Nargo.toml b/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/Nargo.toml
new file mode 100644
index 00000000000..7199d3305bf
--- /dev/null
+++ b/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/Nargo.toml
@@ -0,0 +1,6 @@
+[package]
+name = "ECDSA secp256k1 verification"
+authors = [""]
+compiler_version = "0.1"
+
+[dependencies]
diff --git a/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/Prover.toml b/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/Prover.toml
new file mode 100644
index 00000000000..412c7b36e4c
--- /dev/null
+++ b/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/Prover.toml
@@ -0,0 +1,209 @@
+
+hashed_message = [
+    0x3a,
+    0x73,
+    0xf4,
+    0x12,
+    0x3a,
+    0x5c,
+    0xd2,
+    0x12,
+    0x1f,
+    0x21,
+    0xcd,
+    0x7e,
+    0x8d,
+    0x35,
+    0x88,
+    0x35,
+    0x47,
+    0x69,
+    0x49,
+    0xd0,
+    0x35,
+    0xd9,
+    0xc2,
+    0xda,
+    0x68,
+    0x06,
+    0xb4,
+    0x63,
+    0x3a,
+    0xc8,
+    0xc1,
+    0xe2,
+]
+message = [
+    0x49,
+    0x6e,
+    0x73,
+    0x74,
+    0x72,
+    0x75,
+    0x63,
+    0x74,
+    0x69,
+    0x6f,
+    0x6e,
+    0x73,
+    0x20,
+    0x75,
+    0x6e,
+    0x63,
+    0x6c,
+    0x65,
+    0x61,
+    0x72,
+    0x2c,
+    0x20,
+    0x61,
+    0x73,
+    0x6b,
+    0x20,
+    0x61,
+    0x67,
+    0x61,
+    0x69,
+    0x6e,
+    0x20,
+    0x6c,
+    0x61,
+    0x74,
+    0x65,
+    0x72,
+    0x2e,
+]
+pub_key_x = [
+    0xa0,
+    0x43,
+    0x4d,
+    0x9e,
+    0x47,
+    0xf3,
+    0xc8,
+    0x62,
+    0x35,
+    0x47,
+    0x7c,
+    0x7b,
+    0x1a,
+    0xe6,
+    0xae,
+    0x5d,
+    0x34,
+    0x42,
+    0xd4,
+    0x9b,
+    0x19,
+    0x43,
+    0xc2,
+    0xb7,
+    0x52,
+    0xa6,
+    0x8e,
+    0x2a,
+    0x47,
+    0xe2,
+    0x47,
+    0xc7,
+]
+pub_key_y = [
+    0x89,
+    0x3a,
+    0xba,
+    0x42,
+    0x54,
+    0x19,
+    0xbc,
+    0x27,
+    0xa3,
+    0xb6,
+    0xc7,
+    0xe6,
+    0x93,
+    0xa2,
+    0x4c,
+    0x69,
+    0x6f,
+    0x79,
+    0x4c,
+    0x2e,
+    0xd8,
+    0x77,
+    0xa1,
+    0x59,
+    0x3c,
+    0xbe,
+    0xe5,
+    0x3b,
+    0x03,
+    0x73,
+    0x68,
+    0xd7,
+]
+signature = [
+    0xe5,
+    0x08,
+    0x1c,
+    0x80,
+    0xab,
+    0x42,
+    0x7d,
+    0xc3,
+    0x70,
+    0x34,
+    0x6f,
+    0x4a,
+    0x0e,
+    0x31,
+    0xaa,
+    0x2b,
+    0xad,
+    0x8d,
+    0x97,
+    0x98,
+    0xc3,
+    0x80,
+    0x61,
+    0xdb,
+    0x9a,
+    0xe5,
+    0x5a,
+    0x4e,
+    0x8d,
+    0xf4,
+    0x54,
+    0xfd,
+    0x28,
+    0x11,
+    0x98,
+    0x94,
+    0x34,
+    0x4e,
+    0x71,
+    0xb7,
+    0x87,
+    0x70,
+    0xcc,
+    0x93,
+    0x1d,
+    0x61,
+    0xf4,
+    0x80,
+    0xec,
+    0xbb,
+    0x0b,
+    0x89,
+    0xd6,
+    0xeb,
+    0x69,
+    0x69,
+    0x01,
+    0x61,
+    0xe4,
+    0x9a,
+    0x71,
+    0x5f,
+    0xcd,
+    0x55,
+]
diff --git a/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/src/main.nr b/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/src/main.nr
new file mode 100644
index 00000000000..1cb40f09cd0
--- /dev/null
+++ b/crates/nargo_cli/tests/test_data/ecdsa_secp256k1/src/main.nr
@@ -0,0 +1,11 @@
+use dep::std;
+
+
+fn main(message : [u8;38],hashed_message : [u8;32], pub_key_x : [u8;32], pub_key_y : [u8;32], signature : [u8;64]) {
+     // Hash the message, since secp256k1 expects a hashed_message
+     let expected= std::hash::sha256(message);
+     assert(hashed_message == expected);
+
+     let x = std::ecdsa_secp256k1::verify_signature(pub_key_x, pub_key_y, signature, hashed_message);
+     assert(x == 1);
+}
\ No newline at end of file
diff --git a/crates/nargo_cli/tests/test_data/to_bytes_integration/Prover.toml b/crates/nargo_cli/tests/test_data/to_bytes_integration/Prover.toml
index 07fe857ac7c..23f7acea449 100644
--- a/crates/nargo_cli/tests/test_data/to_bytes_integration/Prover.toml
+++ b/crates/nargo_cli/tests/test_data/to_bytes_integration/Prover.toml
@@ -1 +1,2 @@
 x = "2040124"
+_y = "0x2000000000000000000000000000000000000000000000000000000000000000"
diff --git a/crates/nargo_cli/tests/test_data/to_bytes_integration/src/main.nr b/crates/nargo_cli/tests/test_data/to_bytes_integration/src/main.nr
index 6f57b407da7..36e6d430e2e 100644
--- a/crates/nargo_cli/tests/test_data/to_bytes_integration/src/main.nr
+++ b/crates/nargo_cli/tests/test_data/to_bytes_integration/src/main.nr
@@ -1,14 +1,27 @@
 use dep::std;
 
-fn main(x : Field)  {
+fn main(x : Field, _y: Field)  {
     // The result of this byte array will be big-endian
     let y: Field = 2040124;
     let be_byte_array = y.to_be_bytes(31);
     // The result of this byte array will be little-endian
     let le_byte_array = x.to_le_bytes(31);
     
-    constrain le_byte_array[0] == 60;
-    constrain le_byte_array[0] == be_byte_array[30];
-    constrain le_byte_array[1] == be_byte_array[29];
-    constrain le_byte_array[2] == be_byte_array[28];
+    assert(le_byte_array[0] == 60);
+    assert(le_byte_array[0] == be_byte_array[30]);
+    assert(le_byte_array[1] == be_byte_array[29]);
+    assert(le_byte_array[2] == be_byte_array[28]);
+
+    let z = 0 - 1;
+    let p_bytes = std::field::modulus_le_bytes();
+    let z_bytes = z.to_le_bytes(32);
+    assert(p_bytes[10] == z_bytes[10]);
+    assert(p_bytes[0] == z_bytes[0] as u8 + 1 as u8);
+
+    let p_bits = std::field::modulus_le_bits();
+    let z_bits = z.to_le_bits(std::field::modulus_num_bits() as u32);
+    assert(z_bits[0] == 0);
+    assert(p_bits[100] == z_bits[100]);
+
+   _y.to_le_bits(std::field::modulus_num_bits() as u32);
 }
\ No newline at end of file
diff --git a/crates/noirc_evaluator/src/ssa/acir_gen/constraints.rs b/crates/noirc_evaluator/src/ssa/acir_gen/constraints.rs
index 375ccf1f4dd..5a4176c0893 100644
--- a/crates/noirc_evaluator/src/ssa/acir_gen/constraints.rs
+++ b/crates/noirc_evaluator/src/ssa/acir_gen/constraints.rs
@@ -558,7 +558,8 @@ pub(crate) fn evaluate_constant_modulo(
 ) -> Expression {
     let modulus = FieldElement::from(rhs as i128);
     let modulus_exp = Expression::from_field(modulus);
-    let modulus_bits = bit_size_u128(rhs as u128);
+    assert_ne!(rhs, 0);
+    let modulus_bits = bit_size_u128((rhs - 1) as u128);
     assert!(max_bits >= rhs, "max_bits = {max_bits}, rhs = {rhs}");
     //0. Check for constant expression. This can happen through arithmetic simplifications
     if let Some(a_c) = lhs.to_const() {
@@ -584,8 +585,12 @@ pub(crate) fn evaluate_constant_modulo(
         modulus_bits,
         evaluator,
     );
-    try_range_constraint(b_witness, modulus_bits, evaluator);
-    try_range_constraint(c_witness, max_bits - modulus_bits, evaluator);
+    //if rhs is a power of 2, then we avoid this range check as it is redundant with the previous one.
+    if rhs & (rhs - 1) != 0 {
+        try_range_constraint(b_witness, modulus_bits, evaluator);
+    }
+    let c_bound = FieldElement::modulus() / BigUint::from(rhs) - BigUint::one();
+    try_range_constraint(c_witness, c_bound.bits() as u32, evaluator);
 
     //2. Add the constraint lhs = b+q*rhs
     let b_arith = b_witness.into();