diff --git a/src/bls12_381/ec.rs b/src/bls12_381/ec.rs
index acbdaab..b2b18a9 100644
--- a/src/bls12_381/ec.rs
+++ b/src/bls12_381/ec.rs
@@ -140,7 +140,7 @@ macro_rules! curve_impl {
                 $prepared::from_affine(*self)
             }
 
-            fn to_projective(&self) -> $projective {
+            fn into_projective(&self) -> $projective {
                 (*self).into()
             }
         }
@@ -489,7 +489,7 @@ macro_rules! curve_impl {
                 *self = res;
             }
 
-            fn to_affine(&self) -> $affine {
+            fn into_affine(&self) -> $affine {
                 (*self).into()
             }
 
@@ -980,15 +980,15 @@ pub mod g1 {
         assert!(b.is_valid());
         assert!(c.is_valid());
 
-        let mut tmp1 = a.to_projective();
-        tmp1.add_assign(&b.to_projective());
-        assert_eq!(tmp1.to_affine(), c);
-        assert_eq!(tmp1, c.to_projective());
+        let mut tmp1 = a.into_projective();
+        tmp1.add_assign(&b.into_projective());
+        assert_eq!(tmp1.into_affine(), c);
+        assert_eq!(tmp1, c.into_projective());
 
-        let mut tmp2 = a.to_projective();
+        let mut tmp2 = a.into_projective();
         tmp2.add_assign_mixed(&b);
-        assert_eq!(tmp2.to_affine(), c);
-        assert_eq!(tmp2, c.to_projective());
+        assert_eq!(tmp2.into_affine(), c);
+        assert_eq!(tmp2, c.into_projective());
     }
 
     #[test]
diff --git a/src/bls12_381/tests/mod.rs b/src/bls12_381/tests/mod.rs
index f499d96..6baef49 100644
--- a/src/bls12_381/tests/mod.rs
+++ b/src/bls12_381/tests/mod.rs
@@ -9,7 +9,7 @@ fn test_vectors<G: CurveProjective, E: EncodedPoint<Affine=G::Affine>>(expected:
     {
         let mut expected = expected;
         for _ in 0..1000 {
-            let e_affine = e.to_affine();
+            let e_affine = e.into_affine();
             let encoded = E::from_affine(e_affine).unwrap();
             v.extend_from_slice(encoded.as_ref());
 
diff --git a/src/lib.rs b/src/lib.rs
index 4e27e94..e8c55e1 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -124,7 +124,7 @@ pub trait CurveProjective: PartialEq +
     fn mul_assign<S: Into<<Self::Scalar as PrimeField>::Repr>>(&mut self, other: S);
 
     /// Converts this element into its affine representation.
-    fn to_affine(&self) -> Self::Affine;
+    fn into_affine(&self) -> Self::Affine;
 
     /// Recommends a wNAF window table size given a scalar. Returns `None` if normal
     /// scalar multiplication is encouraged. If `Some` is returned, it will be between
@@ -178,17 +178,17 @@ pub trait CurveAffine: Copy +
     fn prepare(&self) -> Self::Prepared;
 
     /// Converts this element into its affine representation.
-    fn to_projective(&self) -> Self::Projective;
+    fn into_projective(&self) -> Self::Projective;
 
     /// Converts this element into its compressed encoding, so long as it's not
     /// the point at infinity.
-    fn to_compressed(&self) -> Result<Self::Compressed, ()> {
+    fn into_compressed(&self) -> Result<Self::Compressed, ()> {
         <Self::Compressed as EncodedPoint>::from_affine(*self)
     }
 
     /// Converts this element into its uncompressed encoding, so long as it's not
     /// the point at infinity.
-    fn to_uncompressed(&self) -> Result<Self::Uncompressed, ()> {
+    fn into_uncompressed(&self) -> Result<Self::Uncompressed, ()> {
         <Self::Uncompressed as EncodedPoint>::from_affine(*self)
     }
 }
diff --git a/src/tests/curve.rs b/src/tests/curve.rs
index 61ea6c5..86dd81a 100644
--- a/src/tests/curve.rs
+++ b/src/tests/curve.rs
@@ -38,7 +38,7 @@ pub fn curve_tests<G: CurveProjective>()
         let mut z2 = z;
         z2.add_assign(&r);
 
-        z.add_assign_mixed(&r.to_affine());
+        z.add_assign_mixed(&r.into_affine());
 
         assert_eq!(z, z2);
         assert_eq!(z, r);
@@ -47,8 +47,8 @@ pub fn curve_tests<G: CurveProjective>()
     // Transformations
     {
         let a = G::rand(&mut rng);
-        let b = a.to_affine().to_projective();
-        let c = a.to_affine().to_projective().to_affine().to_projective();
+        let b = a.into_affine().into_projective();
+        let c = a.into_affine().into_projective().into_affine().into_projective();
         assert_eq!(a, b);
         assert_eq!(b, c);
     }
@@ -108,7 +108,7 @@ fn random_negation_tests<G: CurveProjective>() {
         assert!(t3.is_zero());
 
         let mut t4 = t1;
-        t4.add_assign_mixed(&t2.to_affine());
+        t4.add_assign_mixed(&t2.into_affine());
         assert!(t4.is_zero());
 
         t1.negate();
@@ -136,7 +136,7 @@ fn random_doubling_tests<G: CurveProjective>() {
         tmp2.add_assign(&b);
 
         let mut tmp3 = a;
-        tmp3.add_assign_mixed(&b.to_affine());
+        tmp3.add_assign_mixed(&b.into_affine());
 
         assert_eq!(tmp1, tmp2);
         assert_eq!(tmp1, tmp3);
@@ -149,8 +149,8 @@ fn random_multiplication_tests<G: CurveProjective>() {
     for _ in 0..1000 {
         let mut a = G::rand(&mut rng);
         let mut b = G::rand(&mut rng);
-        let a_affine = a.to_affine();
-        let b_affine = b.to_affine();
+        let a_affine = a.into_affine();
+        let b_affine = b.into_affine();
 
         let s = G::Scalar::rand(&mut rng);
 
@@ -182,9 +182,9 @@ fn random_addition_tests<G: CurveProjective>() {
         let a = G::rand(&mut rng);
         let b = G::rand(&mut rng);
         let c = G::rand(&mut rng);
-        let a_affine = a.to_affine();
-        let b_affine = b.to_affine();
-        let c_affine = c.to_affine();
+        let a_affine = a.into_affine();
+        let b_affine = b.into_affine();
+        let c_affine = c.into_affine();
 
         // a + a should equal the doubling
         {
@@ -192,7 +192,7 @@ fn random_addition_tests<G: CurveProjective>() {
             aplusa.add_assign(&a);
 
             let mut aplusamixed = a;
-            aplusamixed.add_assign_mixed(&a.to_affine());
+            aplusamixed.add_assign_mixed(&a.into_affine());
 
             let mut adouble = a;
             adouble.double();
@@ -221,17 +221,17 @@ fn random_addition_tests<G: CurveProjective>() {
         // Mixed addition
 
         // (a + b) + c
-        tmp[3] = a_affine.to_projective();
+        tmp[3] = a_affine.into_projective();
         tmp[3].add_assign_mixed(&b_affine);
         tmp[3].add_assign_mixed(&c_affine);
 
         // a + (b + c)
-        tmp[4] = b_affine.to_projective();
+        tmp[4] = b_affine.into_projective();
         tmp[4].add_assign_mixed(&c_affine);
         tmp[4].add_assign_mixed(&a_affine);
 
         // (a + c) + b
-        tmp[5] = a_affine.to_projective();
+        tmp[5] = a_affine.into_projective();
         tmp[5].add_assign_mixed(&c_affine);
         tmp[5].add_assign_mixed(&b_affine);
 
@@ -239,7 +239,7 @@ fn random_addition_tests<G: CurveProjective>() {
         for i in 0..6 {
             for j in 0..6 {
                 assert_eq!(tmp[i], tmp[j]);
-                assert_eq!(tmp[i].to_affine(), tmp[j].to_affine());
+                assert_eq!(tmp[i].into_affine(), tmp[j].into_affine());
             }
 
             assert!(tmp[i] != a);
@@ -258,8 +258,8 @@ fn random_transformation_tests<G: CurveProjective>() {
 
     for _ in 0..1000 {
         let g = G::rand(&mut rng);
-        let g_affine = g.to_affine();
-        let g_projective = g_affine.to_projective();
+        let g_affine = g.into_affine();
+        let g_projective = g_affine.into_projective();
         assert_eq!(g, g_projective);
     }
 
@@ -279,10 +279,10 @@ fn random_transformation_tests<G: CurveProjective>() {
         }
         for _ in 0..5 {
             let s = between.ind_sample(&mut rng);
-            v[s] = v[s].to_affine().to_projective();
+            v[s] = v[s].into_affine().into_projective();
         }
 
-        let expected_v = v.iter().map(|v| v.to_affine().to_projective()).collect::<Vec<_>>();
+        let expected_v = v.iter().map(|v| v.into_affine().into_projective()).collect::<Vec<_>>();
         G::batch_normalization(&mut v);
 
         for i in &v {
@@ -295,25 +295,25 @@ fn random_transformation_tests<G: CurveProjective>() {
 
 fn random_encoding_tests<G: CurveAffine>()
 {
-    assert!(G::zero().to_compressed().is_err());
-    assert!(G::zero().to_uncompressed().is_err());
+    assert!(G::zero().into_compressed().is_err());
+    assert!(G::zero().into_uncompressed().is_err());
 
     let mut rng = XorShiftRng::from_seed([0x5dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
 
     for _ in 0..1000 {
-        let mut r = G::Projective::rand(&mut rng).to_affine();
+        let mut r = G::Projective::rand(&mut rng).into_affine();
 
-        let uncompressed = r.to_uncompressed().unwrap();
+        let uncompressed = r.into_uncompressed().unwrap();
         let de_uncompressed = uncompressed.into_affine().unwrap();
         assert_eq!(de_uncompressed, r);
 
-        let compressed = r.to_compressed().unwrap();
+        let compressed = r.into_compressed().unwrap();
         let de_compressed = compressed.into_affine().unwrap();
         assert_eq!(de_compressed, r);
 
         r.negate();
 
-        let compressed = r.to_compressed().unwrap();
+        let compressed = r.into_compressed().unwrap();
         let de_compressed = compressed.into_affine().unwrap();
         assert_eq!(de_compressed, r);
     }
diff --git a/src/tests/engine.rs b/src/tests/engine.rs
index 5e2c07b..b1bb754 100644
--- a/src/tests/engine.rs
+++ b/src/tests/engine.rs
@@ -10,10 +10,10 @@ pub fn engine_tests<E: Engine>()
         let z1 = E::G1Affine::zero().prepare();
         let z2 = E::G2Affine::zero().prepare();
 
-        let a = E::G1::rand(&mut rng).to_affine().prepare();
-        let b = E::G2::rand(&mut rng).to_affine().prepare();
-        let c = E::G1::rand(&mut rng).to_affine().prepare();
-        let d = E::G2::rand(&mut rng).to_affine().prepare();
+        let a = E::G1::rand(&mut rng).into_affine().prepare();
+        let b = E::G2::rand(&mut rng).into_affine().prepare();
+        let c = E::G1::rand(&mut rng).into_affine().prepare();
+        let d = E::G2::rand(&mut rng).into_affine().prepare();
 
         assert_eq!(
             E::Fqk::one(),
@@ -50,8 +50,8 @@ fn random_miller_loop_tests<E: Engine>() {
 
         let p2 = E::pairing(a, b);
 
-        let a = a.to_affine().prepare();
-        let b = b.to_affine().prepare();
+        let a = a.into_affine().prepare();
+        let b = b.into_affine().prepare();
 
         let p1 = E::final_exponentiation(&E::miller_loop(&[(&a, &b)])).unwrap();
 
@@ -71,10 +71,10 @@ fn random_miller_loop_tests<E: Engine>() {
         let mut abcd = ab;
         abcd.mul_assign(&cd);
 
-        let a = a.to_affine().prepare();
-        let b = b.to_affine().prepare();
-        let c = c.to_affine().prepare();
-        let d = d.to_affine().prepare();
+        let a = a.into_affine().prepare();
+        let b = b.into_affine().prepare();
+        let c = c.into_affine().prepare();
+        let d = d.into_affine().prepare();
 
         let abcd_with_double_loop = E::final_exponentiation(
             &E::miller_loop(&[(&a, &b), (&c, &d)])