diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index 67f8b8c..808284e 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -8,15 +8,14 @@ pub mod arkworks;
 mod ops;
 mod u32;
 
-// The u64 backend requires arkworks
-#[cfg(feature = "arkworks")]
+#[cfg(not(feature = "u32_backend"))]
 mod u64;
 
 cfg_if! {
-    if #[cfg(feature = "arkworks")] {
-        pub type Fp = u64::Fp;
-    } else {
+    if #[cfg(feature = "u32_backend")] {
         pub type Fp = u32::Fp;
+    } else {
+        pub type Fp = u64::Fp;
     }
 }
 
diff --git a/src/fields/fq.rs b/src/fields/fq.rs
index ad5d7cd..9493385 100644
--- a/src/fields/fq.rs
+++ b/src/fields/fq.rs
@@ -8,15 +8,14 @@ pub mod arkworks;
 mod ops;
 mod u32;
 
-// The u64 backend requires arkworks
-#[cfg(feature = "arkworks")]
+#[cfg(not(feature = "u32_backend"))]
 mod u64;
 
 cfg_if! {
-    if #[cfg(feature = "arkworks")] {
-        pub type Fq = u64::Fq;
+    if #[cfg(feature = "u32_backend")] {
+        pub type Fp = u32::Fp;
     } else {
-        pub type Fq = u32::Fq;
+        pub type Fp = u64::Fp;
     }
 }
 
diff --git a/src/fields/fr.rs b/src/fields/fr.rs
index 02a70f4..5edbb7e 100644
--- a/src/fields/fr.rs
+++ b/src/fields/fr.rs
@@ -8,15 +8,14 @@ pub mod arkworks;
 mod ops;
 pub mod u32;
 
-// The u64 backend requires arkworks
-#[cfg(feature = "arkworks")]
+#[cfg(not(feature = "u32_backend"))]
 pub mod u64;
 
 cfg_if! {
-    if #[cfg(feature = "arkworks")] {
-        pub type Fr = u64::Fr;
+    if #[cfg(feature = "u32_backend")] {
+        pub type Fp = u32::Fp;
     } else {
-        pub type Fr = u32::Fr;
+        pub type Fp = u64::Fp;
     }
 }