diff --git a/src/constants.rs b/src/constants.rs
index 955bb8d..4aac26d 100644
--- a/src/constants.rs
+++ b/src/constants.rs
@@ -38,10 +38,12 @@ pub use backend::u64::constants::*;
 #[cfg(not(feature="radix_51"))]
 pub use backend::u32::constants::*;
 
-/// Basepoint has y = 4/5.
+/// The Ed25519 basepoint, in `CompressedEdwardsY` format.
 ///
-/// Generated with Sage: these are the bytes of 4/5 in 𝔽_p.  The
-/// sign bit is 0 since the basepoint has x chosen to be positive.
+/// This is the little-endian byte encoding of \\( 4/5 \pmod p \\),
+/// which is the \\(y\\)-coordinate of the Ed25519 basepoint.
+///
+/// The sign bit is 0 since the basepoint has \\(x\\) chosen to be positive.
 pub const BASE_CMPRSSD: CompressedEdwardsY =
     CompressedEdwardsY([0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
                         0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
@@ -56,12 +58,16 @@ pub const BASE_COMPRESSED_MONTGOMERY: CompressedMontgomeryU =
                            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00]);
 
 
-/// The Ed25519 basepoint, as a `RistrettoPoint`.  This is called `_POINT` to distinguish it from
-/// `_TABLE`, which provides fast scalar multiplication.
+/// The Ristretto basepoint, as a `RistrettoPoint`.
+///
+/// This is called `_POINT` to distinguish it from `_TABLE`, which
+/// provides fast scalar multiplication.
 pub const RISTRETTO_BASEPOINT_POINT: RistrettoPoint = RistrettoPoint(ED25519_BASEPOINT_POINT);
 
-/// `BASEPOINT_ORDER` is the order of base point, i.e. `l = 2^252 +
-/// 27742317777372353535851937790883648493`, in little-endian bytes.
+/// `BASEPOINT_ORDER` is the order of the Ristretto group and of the Ed25519 basepoint, i.e.,
+/// $$
+/// \ell = 2^\{252\} + 27742317777372353535851937790883648493.
+/// $$
 pub const BASEPOINT_ORDER: Scalar = Scalar{
     bytes: [ 
         0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
@@ -78,7 +84,8 @@ include!(concat!(env!("OUT_DIR"), "/basepoint_table.rs"));
 
 #[cfg(feature="precomputed_tables")]
 use ristretto::RistrettoBasepointTable;
-/// The Ed25519 basepoint, as a RistrettoPoint
+
+/// The Ristretto basepoint, as a `RistrettoBasepointTable` for scalar multiplication.
 #[cfg(feature="precomputed_tables")]
 pub const RISTRETTO_BASEPOINT_TABLE: RistrettoBasepointTable
     = RistrettoBasepointTable(ED25519_BASEPOINT_TABLE);