diff --git a/r1cs-std/src/bits/boolean.rs b/r1cs-std/src/bits/boolean.rs
index 4dcde6a..37613f1 100644
--- a/r1cs-std/src/bits/boolean.rs
+++ b/r1cs-std/src/bits/boolean.rs
@@ -308,7 +308,7 @@ impl<ConstraintF: Field> AllocGadget<bool, ConstraintF> for AllocatedBit {
     }
 }
 
-impl<ConstraintF: Field> CondSelectGadget<ConstraintF> for AllocatedBit {
+impl<ConstraintF: PrimeField> CondSelectGadget<ConstraintF> for AllocatedBit {
     fn conditionally_select<CS: ConstraintSystem<ConstraintF>>(
         cs: CS,
         cond: &Boolean,
@@ -328,7 +328,7 @@ impl<ConstraintF: Field> CondSelectGadget<ConstraintF> for AllocatedBit {
     }
 }
 
-fn cond_select_helper<F: Field, CS: ConstraintSystem<F>>(
+fn cond_select_helper<F: PrimeField, CS: ConstraintSystem<F>>(
     mut cs: CS,
     cond: &Boolean,
     first: (Option<bool>, impl Into<ConstraintVar<F>>),
@@ -785,7 +785,8 @@ impl<ConstraintF: Field> ToBytesGadget<ConstraintF> for Boolean {
         self.to_bytes(cs)
     }
 }
-impl<ConstraintF: Field> CondSelectGadget<ConstraintF> for Boolean {
+
+impl<ConstraintF: PrimeField> CondSelectGadget<ConstraintF> for Boolean {
     fn conditionally_select<CS>(
         mut cs: CS,
         cond: &Self,
diff --git a/r1cs-std/src/groups/curves/short_weierstrass/mod.rs b/r1cs-std/src/groups/curves/short_weierstrass/mod.rs
index 967f047..8653bf3 100644
--- a/r1cs-std/src/groups/curves/short_weierstrass/mod.rs
+++ b/r1cs-std/src/groups/curves/short_weierstrass/mod.rs
@@ -91,7 +91,7 @@ impl<P, ConstraintF, F> GroupGadget<SWProjective<P>, ConstraintF>
     for AffineGadget<P, ConstraintF, F>
 where
     P: SWModelParameters,
-    ConstraintF: Field,
+    ConstraintF: PrimeField,
     F: FieldGadget<P::BaseField, ConstraintF>,
 {
     type Value = SWProjective<P>;
@@ -329,7 +329,7 @@ where
 impl<P, ConstraintF, F> CondSelectGadget<ConstraintF> for AffineGadget<P, ConstraintF, F>
 where
     P: SWModelParameters,
-    ConstraintF: Field,
+    ConstraintF: PrimeField,
     F: FieldGadget<P::BaseField, ConstraintF>,
 {
     #[inline]
@@ -424,7 +424,7 @@ impl<P, ConstraintF, F> AllocGadget<SWProjective<P>, ConstraintF>
     for AffineGadget<P, ConstraintF, F>
 where
     P: SWModelParameters,
-    ConstraintF: Field,
+    ConstraintF: PrimeField,
     F: FieldGadget<P::BaseField, ConstraintF>,
 {
     #[inline]