diff --git a/src/constants.rs b/src/constants.rs
index 487d557..1913b8a 100644
--- a/src/constants.rs
+++ b/src/constants.rs
@@ -3141,14 +3141,26 @@ mod test {
 
     #[test]
     fn test_half() {
-        let one = FieldElement([1,0,0,0,0,0,0,0,0,0]);
-        let two = FieldElement([2,0,0,0,0,0,0,0,0,0]);
+        let one = FieldElement::one();
+        let two = &one + &one;
         assert_eq!(one, &two * &constants::HALF);
     }
 
-    #[test]
     /// Test that the constant for sqrt(-486664) really is a square
     /// root of -486664.
+    #[test]
+    #[cfg(feature="radix_51")]
+    fn sqrt_minus_aplus2() {
+        let minus_aplus2 = -&FieldElement([486664,0,0,0,0]);
+        let sqrt = constants::SQRT_MINUS_APLUS2;
+        let sq = &sqrt * &sqrt;
+        assert_eq!(sq, minus_aplus2);
+    }
+
+    /// Test that the constant for sqrt(-486664) really is a square
+    /// root of -486664.
+    #[test]
+    #[cfg(feature="radix_25_5")]
     fn sqrt_minus_aplus2() {
         let minus_aplus2 = FieldElement([-486664,0,0,0,0,0,0,0,0,0]);
         let sqrt = constants::SQRT_MINUS_APLUS2;
@@ -3159,7 +3171,7 @@ mod test {
     #[test]
     /// Test that SQRT_M1 and MSQRT_M1 are square roots of -1
     fn test_sqrt_minus_one() {
-        let minus_one = FieldElement([-1,0,0,0,0,0,0,0,0,0]);
+        let minus_one = FieldElement::minus_one();
         let sqrt_m1_sq = &constants::SQRT_M1 * &constants::SQRT_M1;
         let msqrt_m1_sq = &constants::MSQRT_M1 * &constants::MSQRT_M1;
         assert_eq!(minus_one,  sqrt_m1_sq);
@@ -3168,8 +3180,8 @@ mod test {
 
     #[test]
     fn test_sqrt_constants_sign() {
-        let one       = FieldElement([ 1,0,0,0,0,0,0,0,0,0]);
-        let minus_one = FieldElement([-1,0,0,0,0,0,0,0,0,0]);
+        let one       = FieldElement::one();
+        let minus_one = FieldElement::minus_one();
         let (was_nonzero_square, invsqrt_m1) = minus_one.invsqrt();
         assert_eq!(was_nonzero_square, 1u8);
         let sign_test_sqrt  = &invsqrt_m1 * &constants::SQRT_M1;
@@ -3180,8 +3192,9 @@ mod test {
         assert_eq!(sign_test_msqrt, one);
     }
 
-    #[test]
     /// Test that d = -121665/121666
+    #[cfg(feature="radix_25_5")]
+    #[test]
     fn test_d_vs_ratio() {
         let a = FieldElement([-121665,0,0,0,0,0,0,0,0,0]);
         let b = FieldElement([ 121666,0,0,0,0,0,0,0,0,0]);
@@ -3191,6 +3204,18 @@ mod test {
         assert_eq!(d2, constants::d2);
     }
 
+    /// Test that d = -121665/121666
+    #[cfg(feature="radix_51")]
+    #[test]
+    fn test_d_vs_ratio() {
+        let a = -&FieldElement([121665,0,0,0,0]);
+        let b =   FieldElement([121666,0,0,0,0]);
+        let d = &a * &b.invert();
+        let d2 = &d + &d;
+        assert_eq!(d, constants::d);
+        assert_eq!(d2, constants::d2);
+    }
+
     #[test]
     fn test_d4() {
         let mut four = FieldElement::zero();
@@ -3200,7 +3225,7 @@ mod test {
 
     #[test]
     fn test_a_minus_d() {
-        let a = FieldElement([-1,0,0,0,0,0,0,0,0,0]);
+        let a = FieldElement::minus_one();
         let a_minus_d = &a - &constants::d;
         assert_eq!(a_minus_d, constants::a_minus_d);
     }
diff --git a/src/curve.rs b/src/curve.rs
index 054b164..6bb964a 100644
--- a/src/curve.rs
+++ b/src/curve.rs
@@ -1192,10 +1192,9 @@ mod test {
     /// XXX what does Signal do here?
     #[test]
     fn u_minus_one_monty() {
-        let mut m1 = FieldElement::zero();
-        m1[0] = -1;
-        let m1_bytes = m1.to_bytes();
-        let div_by_zero_u = CompressedMontgomeryU(m1_bytes);
+        let minus_one = FieldElement::minus_one();
+        let minus_one_bytes = minus_one.to_bytes();
+        let div_by_zero_u = CompressedMontgomeryU(minus_one_bytes);
         assert!(div_by_zero_u.decompress().is_none());
     }
 
diff --git a/src/field.rs b/src/field.rs
index 166d604..8bd65ed 100644
--- a/src/field.rs
+++ b/src/field.rs
@@ -267,12 +267,20 @@ impl CTAssignable for FieldElement {
     /// # Preconditions
     ///
     /// * `choice` in {0,1}
+    #[cfg(feature="radix_25_5")]
     fn conditional_assign(&mut self, f: &FieldElement, choice: u8) {
         let mask = -(choice as Limb);
         for i in 0..10 {
             self[i] ^= mask & (self[i] ^ f[i]);
         }
     }
+    #[cfg(feature="radix_51")]
+    fn conditional_assign(&mut self, f: &FieldElement, choice: u8) {
+        let mask = (-(choice as i64)) as u64;
+        for i in 0..5 {
+            self.0[i] ^= mask & (self.0[i] ^ f.0[i]);
+        }
+    }
 }
 
 impl FieldElement {
@@ -283,6 +291,7 @@ impl FieldElement {
             self[i] = -self[i];
         }
     }
+    /// Invert the sign of this field element
     #[cfg(feature="radix_51")]
     pub fn negate(&mut self) {
         // XXX how many copies of p
@@ -293,21 +302,23 @@ impl FieldElement {
         self.0[4] = constants::p.0[4] - self.0[4];
     }
 
-    /// Construct the additive identity
+    /// Construct zero.
     #[cfg(feature="radix_25_5")]
     pub fn zero() -> FieldElement {
         FieldElement([ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ])
     }
+    /// Construct zero.
     #[cfg(feature="radix_51")]
     pub fn zero() -> FieldElement {
         FieldElement([ 0, 0, 0, 0, 0 ])
     }
 
-    /// Construct the multiplicative identity
+    /// Construct one.
     #[cfg(feature="radix_25_5")]
     pub fn one() -> FieldElement {
         FieldElement([ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ])
     }
+    /// Construct one.
     #[cfg(feature="radix_51")]
     pub fn one() -> FieldElement {
         FieldElement([ 1, 0, 0, 0, 0 ])
@@ -318,6 +329,7 @@ impl FieldElement {
     pub fn minus_one() -> FieldElement {
         FieldElement([-1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ])
     }
+    /// Construct -1.
     #[cfg(feature="radix_51")]
     pub fn minus_one() -> FieldElement {
         FieldElement([2251799813685228, 2251799813685247, 2251799813685247, 2251799813685247, 2251799813685247])
@@ -452,6 +464,7 @@ impl FieldElement {
 
         FieldElement::reduce(&h)
     }
+    /// Parse a `FieldElement` from 32 bytes.
     #[cfg(feature="radix_51")]
     pub fn from_bytes(bytes: &[u8;32]) -> FieldElement {
         let low_51_bit_mask = (1u64 << 51) - 1;
@@ -616,6 +629,7 @@ impl FieldElement {
 
         s
     }
+    /// Serialize this `FieldElement` to bytes.
     #[cfg(feature="radix_51")]
     pub fn to_bytes(&self) -> [u8;32] {
         // XXX need to do reduction first
@@ -835,6 +849,7 @@ impl FieldElement {
 
         FieldElement::reduce(&[h0, h1, h2, h3, h4, h5, h6, h7, h8, h9])
     }
+    /// Compute `self * _rhs`.
     #[cfg(feature="radix_51")]
     pub fn multiply(&self, _rhs: &FieldElement) -> FieldElement {
         unimplemented!();
@@ -900,6 +915,7 @@ impl FieldElement {
     pub fn square(&self) -> FieldElement {
         FieldElement::reduce(&self.square_inner())
     }
+    /// Compute `self^2`.
     #[cfg(feature="radix_51")]
     pub fn square(&self) -> FieldElement {
         unimplemented!();
@@ -929,6 +945,7 @@ impl FieldElement {
         }
         FieldElement::reduce(&coeffs)
     }
+    /// Compute `2 * self^2`.
     #[cfg(feature="radix_51")]
     pub fn square2(&self) -> FieldElement {
         unimplemented!();
@@ -1148,6 +1165,7 @@ mod test {
     use field::*;
     use subtle::CTNegatable;
 
+    /*
     #[test]
     fn print_constants() {
         use curve::*;
@@ -1215,8 +1233,9 @@ mod test {
             }
         }
         
-        panic!();
+        //panic!();
     }
+    */
 
     /// Random element a of GF(2^255-19), from Sage
     /// a = 1070314506888354081329385823235218444233221\
@@ -1263,6 +1282,7 @@ mod test {
         assert_eq!(asq, asq_constant_from_sage);
     }
 
+    /*
     #[test]
     fn from_bytes_64_on_a() {
         let a: [u64;5] = [838547684720132, 293808819440897, 1085520638549020, 231251532116217, 416286470530165];
@@ -1271,6 +1291,7 @@ mod test {
         let should_be_a_bytes = to_bytes_64(&a);
         assert_eq!(&A_BYTES, &should_be_a_bytes);
     }
+    */
 
     #[test]
     fn a_square_vs_a_squared_constant() {