diff --git a/src/plonk_common.rs b/src/plonk_common.rs
index 99ba585e..2ae5ec01 100644
--- a/src/plonk_common.rs
+++ b/src/plonk_common.rs
@@ -112,18 +112,20 @@ pub(crate) fn eval_vanishing_poly<F: Extendable<D>, const D: usize>(
 
         // The partial products considered for this iteration of `i`.
         let current_partial_products = &partial_products[i * num_prods..(i + 1) * num_prods];
-        // Check the numerator partial products.
+        // Check the quotient partial products.
         let mut partial_product_check =
             check_partial_products(&quotient_values, current_partial_products, max_degree);
+        // The first checks are of the form `q - n/d` which is a rational function not a polynomial.
+        // We multiply them by `d` to get checks of the form `q*d - n` which low-degree polynomials.
         denominator_values
-            .chunks(max_degree - 1)
+            .chunks(max_degree)
             .zip(partial_product_check.iter_mut())
             .for_each(|(d, q)| {
                 *q *= d.iter().copied().product();
             });
         vanishing_partial_products_terms.extend(partial_product_check);
 
-        // The numerator final product is the product of the last `final_num_prod` elements.
+        // The quotient final product is the product of the last `final_num_prod` elements.
         let quotient: F::Extension = current_partial_products[num_prods - final_num_prod..]
             .iter()
             .copied()
@@ -200,6 +202,8 @@ pub(crate) fn eval_vanishing_poly_base<F: Extendable<D>, const D: usize>(
         // Check the numerator partial products.
         let mut partial_product_check =
             check_partial_products(&quotient_values, current_partial_products, max_degree);
+        // The first checks are of the form `q - n/d` which is a rational function not a polynomial.
+        // We multiply them by `d` to get checks of the form `q*d - n` which low-degree polynomials.
         denominator_values
             .chunks(max_degree)
             .zip(partial_product_check.iter_mut())
@@ -208,7 +212,7 @@ pub(crate) fn eval_vanishing_poly_base<F: Extendable<D>, const D: usize>(
             });
         vanishing_partial_products_terms.extend(partial_product_check);
 
-        // The numerator final product is the product of the last `final_num_prod` elements.
+        // The quotient final product is the product of the last `final_num_prod` elements.
         let quotient: F = current_partial_products[num_prods - final_num_prod..]
             .iter()
             .copied()
@@ -218,7 +222,7 @@ pub(crate) fn eval_vanishing_poly_base<F: Extendable<D>, const D: usize>(
     let vanishing_terms = [
         vanishing_z_1_terms,
         vanishing_partial_products_terms,
-        // vanishing_v_shift_terms,
+        vanishing_v_shift_terms,
         constraint_terms,
     ]
     .concat();
diff --git a/src/prover.rs b/src/prover.rs
index 88cd2b4b..a6f2ce4d 100644
--- a/src/prover.rs
+++ b/src/prover.rs
@@ -90,8 +90,8 @@ pub(crate) fn prove<F: Extendable<D>, const D: usize>(
 
     let plonk_z_vecs = timed!(compute_zs(&partial_products, common_data), "to compute Z's");
 
-    // The first two polynomials in `partial_products` represent the final products used in the
-    // computation of `Z`. They aren't needed anymore so we discard them.
+    // The first polynomial in `partial_products` represent the final product used in the
+    // computation of `Z`. It isn't needed anymore so we discard it.
     partial_products.iter_mut().for_each(|part| {
         part.remove(0);
     });
@@ -313,8 +313,7 @@ fn compute_quotient_polys<'a, F: Extendable<D>, const D: usize>(
         ZeroPolyOnCoset::new(common_data.degree_bits, max_filtered_constraint_degree_bits);
 
     let quotient_values: Vec<Vec<F>> = points
-        // .into_par_iter()
-        .into_iter()
+        .into_par_iter()
         .enumerate()
         .map(|(i, x)| {
             let shifted_x = F::coset_shift() * x;
diff --git a/src/util/partial_products.rs b/src/util/partial_products.rs
index c3e5c2cd..1d169b8d 100644
--- a/src/util/partial_products.rs
+++ b/src/util/partial_products.rs
@@ -5,14 +5,13 @@ use crate::util::ceil_div_usize;
 
 /// Compute partial products of the original vector `v` such that all products consist of `max_degree`
 /// or less elements. This is done until we've computed the product `P` of all elements in the vector.
-/// The final product resulting in `P` consists of at most `max_degree-1` elements since `P` is multiplied
-/// by the `Z` polynomial in the Plonk check.
 pub fn partial_products<T: Product + Copy>(v: &[T], max_degree: usize) -> Vec<T> {
     let mut res = Vec::new();
     let mut remainder = v.to_vec();
     while remainder.len() > max_degree {
         let new_partials = remainder
             .chunks(max_degree)
+            // TODO: can filter out chunks of length 1.
             .map(|chunk| chunk.iter().copied().product())
             .collect::<Vec<_>>();
         res.extend_from_slice(&new_partials);