diff --git a/src/g1.rs b/src/g1.rs
index e9869b73d..f19c03517 100644
--- a/src/g1.rs
+++ b/src/g1.rs
@@ -756,8 +756,9 @@ impl G1Projective {
         xself
     }
 
-    /// Multiplies by $(1 - x)$, which [suffices to clear](https://ia.cr/2019/403)
-    /// the cofactor and map elliptic curve points to elements of $\mathbb{G}\_1$.
+    /// Multiplies by $(1 - z)$, where $z$ is the parameter of BLS12-381, which
+    /// [suffices to clear](https://ia.cr/2019/403) the cofactor and map
+    /// elliptic curve points to elements of $\mathbb{G}\_1$.
     pub fn clear_cofactor(&self) -> G1Projective {
         self - self.mul_by_x()
     }
diff --git a/src/g2.rs b/src/g2.rs
index 1d18dc862..a4d42da05 100644
--- a/src/g2.rs
+++ b/src/g2.rs
@@ -915,9 +915,9 @@ impl G2Projective {
     }
 
     /// Clears the cofactor, using [Budroni-Pintore](https://ia.cr/2017/419).
-    /// This is equivalent to multiplying by:
-    /// $h_\textrm{eff} = 3(x^2 - 1) \cdot h$, where
-    /// $h$ is the cofactor of $\mathbb{G}_2$.
+    /// This is equivalent to multiplying by $h\_\textrm{eff} = 3(z^2 - 1) \cdot
+    /// h_2$, where $h_2$ is the cofactor of $\mathbb{G}\_2$ and $z$ is the
+    /// parameter of BLS12-381.
     pub fn clear_cofactor(&self) -> G2Projective {
         let t1 = self.mul_by_x(); // [x] P
         let t2 = self.psi(); // psi(P)