diff --git a/starky/src/lookup.rs b/starky/src/lookup.rs
index 2a90e6b9..f260400b 100644
--- a/starky/src/lookup.rs
+++ b/starky/src/lookup.rs
@@ -9,7 +9,7 @@ use core::iter::repeat;
 
 use itertools::Itertools;
 use num_bigint::BigUint;
-use plonky2::field::batch_util::batch_add_inplace;
+use plonky2::field::batch_util::{batch_add_inplace, batch_multiply_inplace};
 use plonky2::field::extension::{Extendable, FieldExtension};
 use plonky2::field::packed::PackedField;
 use plonky2::field::polynomial::PolynomialValues;
@@ -761,79 +761,35 @@ pub(crate) fn get_helper_cols<F: Field>(
         .len()
         .div_ceil(constraint_degree.checked_sub(1).unwrap_or(1));
 
-    let mut helper_columns = Vec::with_capacity(num_helper_columns);
-
-    for mut cols_filts in &columns_filters
-        .iter()
-        .chunks(constraint_degree.checked_sub(1).unwrap_or(1))
-    {
-        let (first_col, first_filter) = cols_filts.next().unwrap();
-
-        let mut filter_col = Vec::with_capacity(degree);
-        let first_combined = (0..degree)
-            .map(|d| {
-                let f = {
-                    let f = first_filter.eval_table(trace, d);
-                    filter_col.push(f);
-                    f
-                };
-                if f.is_one() {
-                    let evals = first_col
-                        .iter()
-                        .map(|c| c.eval_table(trace, d))
+    let chunks = columns_filters.chunks(constraint_degree.checked_sub(1).unwrap_or(1));
+    let helper_columns: Vec<_> = chunks
+        .filter_map(|cols_filts| {
+            cols_filts
+                .iter()
+                .map(|(col, filter)| {
+                    let combined = (0..degree)
+                        .map(|d| {
+                            let evals = col
+                                .iter()
+                                .map(|c| c.eval_table(trace, d))
+                                .collect::<Vec<F>>();
+                            challenge.combine(&evals)
+                        })
                         .collect::<Vec<F>>();
-                    challenge.combine(evals.iter())
-                } else {
-                    assert_eq!(f, F::ZERO, "Non-binary filter?");
-                    // Dummy value. Cannot be zero since it will be batch-inverted.
-                    F::ONE
-                }
-            })
-            .collect::<Vec<F>>();
 
-        let mut acc = F::batch_multiplicative_inverse(&first_combined);
-        for d in 0..degree {
-            if filter_col[d].is_zero() {
-                acc[d] = F::ZERO;
-            }
-        }
-
-        for (col, filt) in cols_filts {
-            let mut filter_col = Vec::with_capacity(degree);
-            let mut combined = (0..degree)
-                .map(|d| {
-                    let f = {
-                        let f = filt.eval_table(trace, d);
-                        filter_col.push(f);
-                        f
-                    };
-                    if f.is_one() {
-                        let evals = col
-                            .iter()
-                            .map(|c| c.eval_table(trace, d))
-                            .collect::<Vec<F>>();
-                        challenge.combine(evals.iter())
-                    } else {
-                        assert_eq!(f, F::ZERO, "Non-binary filter?");
-                        // Dummy value. Cannot be zero since it will be batch-inverted.
-                        F::ONE
-                    }
+                    let mut combined = F::batch_multiplicative_inverse(&combined);
+                    let filter_col: Vec<_> =
+                        (0..degree).map(|d| filter.eval_table(trace, d)).collect();
+                    batch_multiply_inplace(&mut combined, &filter_col);
+                    combined
                 })
-                .collect::<Vec<F>>();
-
-            combined = F::batch_multiplicative_inverse(&combined);
-
-            for d in 0..degree {
-                if filter_col[d].is_zero() {
-                    combined[d] = F::ZERO;
-                }
-            }
-
-            batch_add_inplace(&mut acc, &combined);
-        }
-
-        helper_columns.push(acc.into());
-    }
+                .reduce(|mut acc, combined| {
+                    batch_add_inplace(&mut acc, &combined);
+                    acc
+                })
+                .map(PolynomialValues::from)
+        })
+        .collect();
     assert_eq!(helper_columns.len(), num_helper_columns);
 
     helper_columns