diff --git a/examples/signature.rs b/examples/signature.rs
index 90438df..6818a4c 100644
--- a/examples/signature.rs
+++ b/examples/signature.rs
@@ -57,7 +57,7 @@ where
     let mut t = [0u8; 80];
     rng.fill_bytes(&mut t[..]);
 
-    // h = H*(T || M)
+    // h = H(T || M)
     let h = Self::hash_to_scalar(b"Nova_Ecdsa_Hash", &t[..], c.to_repr().as_mut());
 
     // R = [h]G
diff --git a/src/gadgets/r1cs.rs b/src/gadgets/r1cs.rs
index 6841d71..4a4fced 100644
--- a/src/gadgets/r1cs.rs
+++ b/src/gadgets/r1cs.rs
@@ -120,7 +120,7 @@ impl<G: Group> AllocatedRelaxedR1CSInstance<G> {
   }
 
   /// Allocates the hardcoded default RelaxedR1CSInstance in the circuit.
-  /// W = E = 0, u = 1, X0 = X1 = 0
+  /// W = E = 0, u = 0, X0 = X1 = 0
   pub fn default<CS: ConstraintSystem<<G as Group>::Base>>(
     mut cs: CS,
     limb_width: usize,
diff --git a/src/nifs.rs b/src/nifs.rs
index 89633e7..4f2d5ef 100644
--- a/src/nifs.rs
+++ b/src/nifs.rs
@@ -78,7 +78,7 @@ impl<G: Group> NIFS<G> {
     ))
   }
 
-  /// Takes as input a relaxed R1CS instance `U1` and and R1CS instance `U2`
+  /// Takes as input a relaxed R1CS instance `U1` and R1CS instance `U2`
   /// with the same shape and defined with respect to the same parameters,
   /// and outputs a folded instance `U` with the same shape,
   /// with the guarantee that the folded instance `U`