diff --git a/src/edwards.rs b/src/edwards.rs
index 2706c43..664dfe7 100644
--- a/src/edwards.rs
+++ b/src/edwards.rs
@@ -176,12 +176,12 @@ impl Debug for CompressedEdwardsY {
 
 impl CompressedEdwardsY {
     /// View this `CompressedEdwardsY` as an array of bytes.
-    pub fn as_bytes(&self) -> &[u8; 32] {
+    pub const fn as_bytes(&self) -> &[u8; 32] {
         &self.0
     }
 
     /// Copy this `CompressedEdwardsY` to an array of bytes.
-    pub fn to_bytes(&self) -> [u8; 32] {
+    pub const fn to_bytes(&self) -> [u8; 32] {
         self.0
     }
 
@@ -481,7 +481,7 @@ impl EdwardsPoint {
     /// coordinates to projective coordinates.
     ///
     /// Free.
-    pub(crate) fn as_projective(&self) -> ProjectivePoint {
+    pub(crate) const fn as_projective(&self) -> ProjectivePoint {
         ProjectivePoint {
             X: self.X,
             Y: self.Y,
diff --git a/src/montgomery.rs b/src/montgomery.rs
index 09653c0..a1143d0 100644
--- a/src/montgomery.rs
+++ b/src/montgomery.rs
@@ -119,12 +119,12 @@ impl Zeroize for MontgomeryPoint {
 
 impl MontgomeryPoint {
     /// View this `MontgomeryPoint` as an array of bytes.
-    pub fn as_bytes(&self) -> &[u8; 32] {
+    pub const fn as_bytes(&self) -> &[u8; 32] {
         &self.0
     }
 
     /// Convert this `MontgomeryPoint` to an array of bytes.
-    pub fn to_bytes(&self) -> [u8; 32] {
+    pub const fn to_bytes(&self) -> [u8; 32] {
         self.0
     }
 
diff --git a/src/ristretto.rs b/src/ristretto.rs
index cbca349..3df1766 100644
--- a/src/ristretto.rs
+++ b/src/ristretto.rs
@@ -231,12 +231,12 @@ impl ConstantTimeEq for CompressedRistretto {
 
 impl CompressedRistretto {
     /// Copy the bytes of this `CompressedRistretto`.
-    pub fn to_bytes(&self) -> [u8; 32] {
+    pub const fn to_bytes(&self) -> [u8; 32] {
         self.0
     }
 
     /// View this `CompressedRistretto` as an array of bytes.
-    pub fn as_bytes(&self) -> &[u8; 32] {
+    pub const fn as_bytes(&self) -> &[u8; 32] {
         &self.0
     }
 
diff --git a/src/scalar.rs b/src/scalar.rs
index d5266cc..0f27b0c 100644
--- a/src/scalar.rs
+++ b/src/scalar.rs
@@ -226,8 +226,9 @@ pub struct Scalar {
     ///
     /// This ensures that there is room for a carry bit when computing a NAF representation.
     //
-    // XXX This is pub(crate) so we can write literal constants.  If const fns were stable, we could
-    //     make the Scalar constructors const fns and use those instead.
+    // XXX This is pub(crate) so we can write literal constants.
+    //     Alternatively we could make the Scalar constructors `const fn`s and use those instead.
+    //     See dalek-cryptography/curve25519-dalek#493
     pub(crate) bytes: [u8; 32],
 }
 
@@ -688,7 +689,7 @@ impl Scalar {
     ///
     /// assert!(s.to_bytes() == [0u8; 32]);
     /// ```
-    pub fn to_bytes(&self) -> [u8; 32] {
+    pub const fn to_bytes(&self) -> [u8; 32] {
         self.bytes
     }
 
@@ -703,7 +704,7 @@ impl Scalar {
     ///
     /// assert!(s.as_bytes() == &[0u8; 32]);
     /// ```
-    pub fn as_bytes(&self) -> &[u8; 32] {
+    pub const fn as_bytes(&self) -> &[u8; 32] {
         &self.bytes
     }