diff --git a/halo2_gadgets/src/sinsemilla.rs b/halo2_gadgets/src/sinsemilla.rs
index 2a9c92a79c..71f7d27a58 100644
--- a/halo2_gadgets/src/sinsemilla.rs
+++ b/halo2_gadgets/src/sinsemilla.rs
@@ -442,9 +442,8 @@ where
     }
 
     #[allow(clippy::type_complexity)]
-    /// $\mathsf{SinsemillaCommit}$ from [§ 5.4.8.4][concretesinsemillacommit].
-    ///
-    /// [concretesinsemillacommit]: https://zips.z.cash/protocol/nu5.pdf#concretesinsemillacommit
+    /// Evaluates the Sinsemilla hash of `message` from the public initial point `Q` stored
+    /// into `CommitDomain`.
     pub fn hash(
         &self,
         layouter: impl Layouter<C::Base>,
@@ -462,9 +461,7 @@ where
 
     #[allow(non_snake_case)]
     #[allow(clippy::type_complexity)]
-    /// $\mathsf{SinsemillaCommit}$ from [§ 5.4.8.4][concretesinsemillacommit].
-    ///
-    /// [concretesinsemillacommit]: https://zips.z.cash/protocol/nu5.pdf#concretesinsemillacommit
+    /// Evaluates the Sinsemilla hash of `message` from the private initial point `Q`.
     pub fn hash_with_private_init(
         &self,
         layouter: impl Layouter<C::Base>,
@@ -482,17 +479,13 @@ where
     }
 
     #[allow(clippy::type_complexity)]
-    /// $\mathsf{SinsemillaCommit}$ from [§ 5.4.8.4][concretesinsemillacommit].
-    ///
-    /// [concretesinsemillacommit]: https://zips.z.cash/protocol/nu5.pdf#concretesinsemillacommit
+    /// Returns the public initial point `Q` stored into `CommitDomain`.
     pub fn q_init(&self) -> C {
         self.M.Q
     }
 
     #[allow(clippy::type_complexity)]
-    /// $\mathsf{SinsemillaCommit}$ from [§ 5.4.8.4][concretesinsemillacommit].
-    ///
-    /// [concretesinsemillacommit]: https://zips.z.cash/protocol/nu5.pdf#concretesinsemillacommit
+    /// Evaluates the blinding factor equal to $[r] R$ where `r` is stored in the `CommitDomain`.
     pub fn blinding_factor(
         &self,
         mut layouter: impl Layouter<C::Base>,
diff --git a/halo2_gadgets/src/sinsemilla/chip/generator_table.rs b/halo2_gadgets/src/sinsemilla/chip/generator_table.rs
index 13773a4659..002045e751 100644
--- a/halo2_gadgets/src/sinsemilla/chip/generator_table.rs
+++ b/halo2_gadgets/src/sinsemilla/chip/generator_table.rs
@@ -78,6 +78,22 @@ impl GeneratorTableConfig {
         });
     }
 
+    /// Load the generator table into the circuit.
+    ///
+    /// | table_idx |    table_x   |    table_y   | table_range_check_tag |
+    /// -------------------------------------------------------------------
+    /// |     0     |    X(S[0])   |    Y(S[0])   |           0           |
+    /// |     1     |    X(S[1])   |    Y(S[1])   |           0           |
+    /// |    ...    |      ...     |      ...     |           0           |
+    /// |   2^10-1  | X(S[2^10-1]) | Y(S[2^10-1]) |           0           |
+    /// |     0     |    X(S[0])   |    Y(S[0])   |           4           |
+    /// |     1     |    X(S[1])   |    Y(S[1])   |           4           |
+    /// |    ...    |      ...     |      ...     |           4           |
+    /// |   2^4-1   | X(S[2^4-1])  | Y(S[2^4-1])  |           4           |
+    /// |     0     |    X(S[0])   |    Y(S[0])   |           5           |
+    /// |     1     |    X(S[1])   |    Y(S[1])   |           5           |
+    /// |    ...    |      ...     |      ...     |           5           |
+    /// |   2^5-1   | X(S[2^5-1])  | Y(S[2^5-1])  |           5           |
     pub fn load(&self, layouter: &mut impl Layouter<pallas::Base>) -> Result<(), Error> {
         layouter.assign_table(
             || "generator_table",
diff --git a/halo2_gadgets/src/sinsemilla/chip/hash_to_point.rs b/halo2_gadgets/src/sinsemilla/chip/hash_to_point.rs
index 771d2a9c5f..226e5e8a05 100644
--- a/halo2_gadgets/src/sinsemilla/chip/hash_to_point.rs
+++ b/halo2_gadgets/src/sinsemilla/chip/hash_to_point.rs
@@ -253,9 +253,6 @@ where
 
     #[allow(clippy::type_complexity)]
     /// Hash `message` from the initial point `Q`.
-    ///
-    /// Before this call to `hash_all_pieces()`, `x_Q` and `y_Q` MUST have been already assigned
-    /// within this region.
     fn hash_all_pieces(
         &self,
         region: &mut Region<'_, pallas::Base>,
diff --git a/halo2_gadgets/src/utilities/lookup_range_check.rs b/halo2_gadgets/src/utilities/lookup_range_check.rs
index d1173babbc..64b4ce4c90 100644
--- a/halo2_gadgets/src/utilities/lookup_range_check.rs
+++ b/halo2_gadgets/src/utilities/lookup_range_check.rs
@@ -150,7 +150,7 @@ impl<F: PrimeFieldBits, const K: usize> LookupRangeCheckConfig<F, K> {
                     * q_range_check_4
                     * Expression::Constant(F::from(4_u64));
 
-            // Combine the running sum and short lookups:
+            // Combine the running sum, short lookups and optimized range checks:
             vec![
                 (
                     q_lookup.clone()