diff --git a/src/arithmetic/curves.rs b/src/arithmetic/curves.rs
index f9b2ef4..ade9dbf 100644
--- a/src/arithmetic/curves.rs
+++ b/src/arithmetic/curves.rs
@@ -102,9 +102,9 @@ pub trait CurveAffine:
     + From<<Self as PrimeCurveAffine>::Curve>
 {
     /// The scalar field of this elliptic curve.
-    type ScalarExt: FieldExt;
+    type ScalarExt: FieldExt + Ord;
     /// The base field over which this elliptic curve is constructed.
-    type Base: FieldExt;
+    type Base: FieldExt + Ord;
     /// The projective form of the curve
     type CurveExt: CurveExt<AffineExt = Self, ScalarExt = <Self as CurveAffine>::ScalarExt>;
 
diff --git a/src/arithmetic/fields.rs b/src/arithmetic/fields.rs
index ef45018..d42419d 100644
--- a/src/arithmetic/fields.rs
+++ b/src/arithmetic/fields.rs
@@ -30,7 +30,7 @@ pub(crate) trait SqrtTableHelpers: ff::PrimeField {
 
 /// This trait is a common interface for dealing with elements of a finite
 /// field.
-pub trait FieldExt: ff::WithSmallOrderMulGroup<3> + Ord {}
+pub trait FieldExt: ff::WithSmallOrderMulGroup<3> {}
 
 /// Parameters for a perfect hash function used in square root computation.
 #[cfg(feature = "sqrt-table")]