diff --git a/src/fq.rs b/src/fq.rs
index 2aeaab0..e31b32f 100644
--- a/src/fq.rs
+++ b/src/fq.rs
@@ -109,14 +109,7 @@ impl<'a, 'b> Add<&'b Fq> for &'a Fq {
 
     #[inline]
     fn add(self, rhs: &'b Fq) -> Fq {
-        let (d0, carry) = adc(self.0[0], rhs.0[0], 0);
-        let (d1, carry) = adc(self.0[1], rhs.0[1], carry);
-        let (d2, carry) = adc(self.0[2], rhs.0[2], carry);
-        let (d3, _) = adc(self.0[3], rhs.0[3], carry);
-
-        // Attempt to subtract the modulus, to ensure the value
-        // is smaller than the modulus.
-        Fq([d0, d1, d2, d3]) - &MODULUS
+        self.field_add(rhs)
     }
 }
 
@@ -554,7 +547,7 @@ impl Fq {
     }
 
     #[inline]
-    const fn multiply(&self, rhs: &Self) -> Self {
+    pub(crate) const fn multiply(&self, rhs: &Self) -> Self {
         // Schoolbook multiplication
 
         let (r0, carry) = mac(0, self.0[0], rhs.0[0], 0);
@@ -581,7 +574,7 @@ impl Fq {
     }
 
     #[inline]
-    const fn subtract(&self, rhs: &Self) -> Self {
+    pub(crate) const fn subtract(&self, rhs: &Self) -> Self {
         let (d0, borrow) = sbb(self.0[0], rhs.0[0], 0);
         let (d1, borrow) = sbb(self.0[1], rhs.0[1], borrow);
         let (d2, borrow) = sbb(self.0[2], rhs.0[2], borrow);
@@ -596,6 +589,18 @@ impl Fq {
 
         Fq([d0, d1, d2, d3])
     }
+
+    #[inline]
+    pub(crate) const fn field_add(&self, rhs: &Self) -> Self {
+        let (d0, carry) = adc(self.0[0], rhs.0[0], 0);
+        let (d1, carry) = adc(self.0[1], rhs.0[1], carry);
+        let (d2, carry) = adc(self.0[2], rhs.0[2], carry);
+        let (d3, _) = adc(self.0[3], rhs.0[3], carry);
+
+        // Attempt to subtract the modulus, to ensure the value
+        // is smaller than the modulus.
+        Fq([d0, d1, d2, d3]).subtract(&MODULUS)
+    }
 }
 
 impl<'a> From<&'a Fq> for [u8; 32] {
diff --git a/src/lib.rs b/src/lib.rs
index 93c356d..515ec7b 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -371,11 +371,11 @@ impl AffinePoint {
 
     /// Performs a pre-processing step that produces an `AffineNielsPoint`
     /// for use in multiple additions.
-    pub fn to_niels(&self) -> AffineNielsPoint {
+    pub const fn to_niels(&self) -> AffineNielsPoint {
         AffineNielsPoint {
-            v_plus_u: &self.v + &self.u,
-            v_minus_u: &self.v - &self.u,
-            t2d: &self.u * &self.v * EDWARDS_D2,
+            v_plus_u: self.v.field_add(&self.u),
+            v_minus_u: self.v.subtract(&self.u),
+            t2d: self.u.multiply(&self.v).multiply(&EDWARDS_D2)
         }
     }