diff --git a/field/src/extension/quadratic.rs b/field/src/extension/quadratic.rs
index c0c9758b..281369d2 100644
--- a/field/src/extension/quadratic.rs
+++ b/field/src/extension/quadratic.rs
@@ -109,6 +109,14 @@ impl<F: Extendable<2>> Field for QuadraticExtension<F> {
     fn from_noncanonical_u128(n: u128) -> Self {
         F::from_noncanonical_u128(n).into()
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        F::from_noncanonical_i64(n).into()
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        F::from_noncanonical_u64(n).into()
+    }
 }
 
 impl<F: Extendable<2>> Display for QuadraticExtension<F> {
diff --git a/field/src/extension/quartic.rs b/field/src/extension/quartic.rs
index e7aba63b..8c8a9e7e 100644
--- a/field/src/extension/quartic.rs
+++ b/field/src/extension/quartic.rs
@@ -119,6 +119,14 @@ impl<F: Extendable<4>> Field for QuarticExtension<F> {
     fn from_noncanonical_u128(n: u128) -> Self {
         F::from_noncanonical_u128(n).into()
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        F::from_noncanonical_i64(n).into()
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        F::from_noncanonical_u64(n).into()
+    }
 }
 
 impl<F: Extendable<4>> Display for QuarticExtension<F> {
diff --git a/field/src/extension/quintic.rs b/field/src/extension/quintic.rs
index d4b605eb..28ec9226 100644
--- a/field/src/extension/quintic.rs
+++ b/field/src/extension/quintic.rs
@@ -126,6 +126,14 @@ impl<F: Extendable<5>> Field for QuinticExtension<F> {
     fn from_noncanonical_u128(n: u128) -> Self {
         F::from_noncanonical_u128(n).into()
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        F::from_noncanonical_i64(n).into()
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        F::from_noncanonical_u64(n).into()
+    }
 }
 
 impl<F: Extendable<5>> Display for QuinticExtension<F> {
diff --git a/field/src/secp256k1_base.rs b/field/src/secp256k1_base.rs
index eaa964f8..bf4cbe61 100644
--- a/field/src/secp256k1_base.rs
+++ b/field/src/secp256k1_base.rs
@@ -142,6 +142,15 @@ impl Field for Secp256K1Base {
     fn from_noncanonical_u96(n: (u64, u32)) -> Self {
         Self([n.0, n.1 as u64, 0, 0])
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        let f = Self::from_canonical_u64(n.unsigned_abs());
+        if n < 0 { -f } else { f }
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        Self::from_canonical_u64(n)
+    }
 }
 
 impl PrimeField for Secp256K1Base {
diff --git a/field/src/secp256k1_scalar.rs b/field/src/secp256k1_scalar.rs
index 1f1de697..b4494681 100644
--- a/field/src/secp256k1_scalar.rs
+++ b/field/src/secp256k1_scalar.rs
@@ -150,6 +150,15 @@ impl Field for Secp256K1Scalar {
     fn from_noncanonical_u96(n: (u64, u32)) -> Self {
         Self([n.0, n.1 as u64, 0, 0])
     }
+
+    fn from_noncanonical_i64(n: i64) -> Self {
+        let f = Self::from_canonical_u64(n.unsigned_abs());
+        if n < 0 { -f } else { f }
+    }
+
+    fn from_noncanonical_u64(n: u64) -> Self {
+        Self::from_canonical_u64(n)
+    }
 }
 
 impl PrimeField for Secp256K1Scalar {
diff --git a/field/src/types.rs b/field/src/types.rs
index 2c0d15c7..646dff73 100644
--- a/field/src/types.rs
+++ b/field/src/types.rs
@@ -342,24 +342,10 @@ pub trait Field:
     fn from_noncanonical_u128(n: u128) -> Self;
 
     /// Returns `x % Self::CHARACTERISTIC`.
-    ///
-    /// Implemented by default via `from_noncanonical_u128`
-    /// Override, if you have a faster implementation for your field.
-    fn from_noncanonical_u64(n: u64) -> Self {
-        Self::from_noncanonical_u128(n as u128)
-    }
+    fn from_noncanonical_u64(n: u64) -> Self;
 
     /// Returns `n` as an element of this field.
-    ///
-    /// Implemented by default via `from_noncanonical_u128` and case analysis.
-    /// Override, if you have a faster implementation for your field.
-    fn from_noncanonical_i64(n: i64) -> Self {
-        if n < 0 {
-            -Self::from_noncanonical_u128((n as i128).unsigned_abs())
-        } else {
-            Self::from_noncanonical_u128(n as u128)
-        }
-    }
+    fn from_noncanonical_i64(n: i64) -> Self;
 
     /// Returns `n % Self::characteristic()`. May be cheaper than from_noncanonical_u128 when we know
     /// that `n < 2 ** 96`.