diff --git a/src/backend/u32/constants.rs b/src/backend/u32/constants.rs
index 94702d7..f68f662 100644
--- a/src/backend/u32/constants.rs
+++ b/src/backend/u32/constants.rs
@@ -46,22 +46,11 @@ pub(crate) const SQRT_M1: FieldElement32 = FieldElement32([
     33281959, 41962654, 31548777,  326685, 11406482,
 ]);
 
-/// In Montgomery form y² = x³+Ax²+x, Curve25519 has A=486662.
-pub(crate) const MONTGOMERY_A: FieldElement32 = FieldElement32([
-    486662, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-]);
-
 /// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
 pub(crate) const APLUS2_OVER_FOUR: FieldElement32 = FieldElement32([
     121666, 0, 0, 0, 0, 0, 0, 0, 0, 0
 ]);
 
-/// `SQRT_MINUS_APLUS2` is sqrt(-486664)
-pub(crate) const SQRT_MINUS_APLUS2: FieldElement32 = FieldElement32([
-    54885894, 25242303, 55597453,  9067496, 51808079,
-    33312638, 25456129, 14121551, 54921728,  3972023,
-]);
-
 /// `L` is the order of base point, i.e. 2^252 +
 /// 27742317777372353535851937790883648493
 pub(crate) const L: Scalar32 = Scalar32([ 0x1cf5d3ed, 0x009318d2, 0x1de73596, 0x1df3bd45,
diff --git a/src/backend/u64/constants.rs b/src/backend/u64/constants.rs
index 254c81c..1cc23fa 100644
--- a/src/backend/u64/constants.rs
+++ b/src/backend/u64/constants.rs
@@ -33,15 +33,9 @@ pub(crate) const INVSQRT_A_MINUS_D: FieldElement64 = FieldElement64([
 /// Precomputed value of one of the square roots of -1 (mod p)
 pub(crate) const SQRT_M1: FieldElement64 = FieldElement64([1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133]);
 
-/// In Montgomery form y² = x³+Ax²+x, Curve25519 has A=486662.
-pub(crate) const MONTGOMERY_A: FieldElement64 = FieldElement64([486662, 0, 0, 0, 0]);
-
 /// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
 pub(crate) const APLUS2_OVER_FOUR: FieldElement64 = FieldElement64([121666, 0, 0, 0, 0]);
 
-/// `SQRT_MINUS_APLUS2` is sqrt(-486664)
-pub(crate) const SQRT_MINUS_APLUS2: FieldElement64 = FieldElement64([1693982333959686, 608509411481997, 2235573344831311, 947681270984193, 266558006233600]);
-
 /// `L` is the order of base point, i.e. 2^252 + 27742317777372353535851937790883648493
 pub(crate) const L: Scalar64 = Scalar64([ 0x0002631a5cf5d3ed, 0x000dea2f79cd6581, 0x000000000014def9, 0x0000000000000000, 0x0000100000000000 ]);
 
diff --git a/src/constants.rs b/src/constants.rs
index 9da0800..c8cf1c1 100644
--- a/src/constants.rs
+++ b/src/constants.rs
@@ -129,30 +129,6 @@ mod test {
         }
     }
 
-    /// Test that the constant for sqrt(-486664) really is a square
-    /// root of -486664.
-    #[test]
-    #[cfg(feature="radix_51")]
-    fn sqrt_minus_aplus2() {
-        use backend::u64::field::FieldElement64;
-        let minus_aplus2 = -&FieldElement64([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(not(feature="radix_51"))]
-    fn sqrt_minus_aplus2() {
-        use backend::u32::field::FieldElement32;
-        let minus_aplus2 = -&FieldElement32([486664,0,0,0,0,0,0,0,0,0]);
-        let sqrt = constants::SQRT_MINUS_APLUS2;
-        let sq = &sqrt * &sqrt;
-        assert_eq!(sq, minus_aplus2);
-    }
-
     #[test]
     /// Test that SQRT_M1 is a square root of -1
     fn test_sqrt_minus_one() {
diff --git a/src/montgomery.rs b/src/montgomery.rs
index 8ba7670..81337c5 100644
--- a/src/montgomery.rs
+++ b/src/montgomery.rs
@@ -50,13 +50,12 @@
 
 use core::ops::{Mul, MulAssign};
 
-use constants;
 use constants::APLUS2_OVER_FOUR;
 use field::FieldElement;
 use edwards::{EdwardsPoint, CompressedEdwardsY};
 use scalar::Scalar;
 
-use traits::{Identity, ValidityCheck};
+use traits::Identity;
 
 use subtle::ConditionallyAssignable;
 use subtle::ConditionallySwappable;
@@ -277,8 +276,7 @@ impl Mul<MontgomeryPoint> for Scalar {
 
 #[cfg(test)]
 mod test {
-    use constants::X25519_BASEPOINT;
-    use traits::Identity;
+    use constants;
     use super::*;
 
     use rand::OsRng;
diff --git a/src/scalar.rs b/src/scalar.rs
index c2b177b..34e1776 100644
--- a/src/scalar.rs
+++ b/src/scalar.rs
@@ -715,24 +715,6 @@ mod test {
             0xe8, 0xef, 0x7a, 0xc3, 0x1f, 0x35, 0xbb, 0x05,
         ],
     };
-    /// z = 5033871415930814945849241457262266927579821285980625165479289807629491019013
-    pub static Z: Scalar = Scalar{
-        bytes: [
-            0x05, 0x9d, 0x3e, 0x0b, 0x09, 0x26, 0x50, 0x3d,
-            0xa3, 0x84, 0xa1, 0x3c, 0x92, 0x7a, 0xc2, 0x06,
-            0x41, 0x98, 0xcf, 0x34, 0x3a, 0x24, 0xd5, 0xb7,
-            0xeb, 0x33, 0x6a, 0x2d, 0xfc, 0x11, 0x21, 0x0b,
-        ],
-    };
-    /// w = 3486911242272497535104403593250518247409663771668155364040899665266216860804
-    static W: Scalar = Scalar{
-        bytes: [
-            0x84, 0xfc, 0xbc, 0x4f, 0x78, 0x12, 0xa0, 0x06,
-            0xd7, 0x91, 0xd9, 0x7a, 0x3a, 0x27, 0xdd, 0x1e,
-            0x21, 0x43, 0x45, 0xf7, 0xb1, 0xb9, 0x56, 0x7a,
-            0x81, 0x30, 0x73, 0x44, 0x96, 0x85, 0xb5, 0x07,
-        ],
-    };
 
     /// x*y = 5690045403673944803228348699031245560686958845067437804563560795922180092780
     static X_TIMES_Y: Scalar = Scalar{