diff --git a/plonky2/src/gadgets/nonnative.rs b/plonky2/src/gadgets/nonnative.rs
index 83333491..8726fde7 100644
--- a/plonky2/src/gadgets/nonnative.rs
+++ b/plonky2/src/gadgets/nonnative.rs
@@ -146,12 +146,24 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         a: &NonNativeTarget<FF>,
         b: &NonNativeTarget<FF>,
     ) -> NonNativeTarget<FF> {
-        let order = self.constant_biguint(&FF::order());
-        let a_plus_order = self.add_biguint(&order, &a.value);
-        let result = self.sub_biguint(&a_plus_order, &b.value);
+        let diff = self.add_virtual_nonnative_target::<FF>();
+        let overflow = self.add_virtual_bool_target();
 
-        // TODO: reduce sub result with only one conditional addition?
-        self.reduce(&result)
+        self.add_simple_generator(NonNativeSubtractionGenerator::<F, D, FF> {
+            a: a.clone(),
+            b: b.clone(),
+            diff: diff.clone(),
+            overflow: overflow.clone(),
+            _phantom: PhantomData,
+        });
+
+        let diff_plus_b = self.add_biguint(&diff.value, &b.value);
+        let modulus = self.constant_biguint(&FF::order());
+        let mod_times_overflow = self.mul_biguint_by_bool(&modulus, overflow);
+        let diff_plus_b_reduced = self.sub_biguint(&diff_plus_b, &mod_times_overflow);
+        self.connect_biguint(&a.value, &diff_plus_b_reduced);
+
+        diff
     }
 
     pub fn mul_nonnative<FF: Field>(
@@ -363,6 +375,47 @@ impl<F: RichField + Extendable<D>, const D: usize, FF: Field> SimpleGenerator<F>
     }
 }
 
+#[derive(Debug)]
+struct NonNativeSubtractionGenerator<F: RichField + Extendable<D>, const D: usize, FF: Field> {
+    a: NonNativeTarget<FF>,
+    b: NonNativeTarget<FF>,
+    diff: NonNativeTarget<FF>,
+    overflow: BoolTarget,
+    _phantom: PhantomData<F>,
+}
+
+impl<F: RichField + Extendable<D>, const D: usize, FF: Field> SimpleGenerator<F>
+    for NonNativeSubtractionGenerator<F, D, FF>
+{
+    fn dependencies(&self) -> Vec<Target> {
+        self.a
+            .value
+            .limbs
+            .iter()
+            .cloned()
+            .chain(self.b.value.limbs.clone())
+            .map(|l| l.0)
+            .collect()
+    }
+
+    fn run_once(&self, witness: &PartitionWitness<F>, out_buffer: &mut GeneratedValues<F>) {
+        let a = witness.get_nonnative_target(self.a.clone());
+        let b = witness.get_nonnative_target(self.b.clone());
+        let a_biguint = a.to_biguint();
+        let b_biguint = b.to_biguint();
+
+        let modulus = FF::order();
+        let (diff_biguint, overflow) = if a_biguint > b_biguint {
+            (a_biguint - b_biguint, false)
+        } else {
+            (modulus + a_biguint - b_biguint, true)
+        };
+
+        out_buffer.set_biguint_target(self.diff.value.clone(), diff_biguint);
+        out_buffer.set_bool_target(self.overflow, overflow);
+    }
+}
+
 #[derive(Debug)]
 struct NonNativeInverseGenerator<F: RichField + Extendable<D>, const D: usize, FF: Field> {
     x: NonNativeTarget<FF>,