diff --git a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover_internal.hpp b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover_internal.hpp
index efad2d0e072..c635da8cfa2 100644
--- a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover_internal.hpp
+++ b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover_internal.hpp
@@ -161,6 +161,36 @@ template <class DeciderProvingKeys_> class ProtogalaxyProverInternal {
 
         return aggregated_relation_evaluations;
     }
+
+    /**
+     * @brief Initialise the data structured storing a set of nodes at a given level, in parallel if the width is
+     * sufficiently big
+     *
+     * @param level_width determines the number of nodes for the given level
+     * @param degree determines the degree of the polynomial stored in each node, the number of elements will be
+     * degree+1
+     *
+     * @return std::vector<std::vector<FF>>
+     */
+    static std::vector<std::vector<FF>> initialise_coefficient_tree_level(const size_t level_width, const size_t degree)
+    {
+        PROFILE_THIS_NAME("initialise coefficient tree level");
+        std::vector<std::vector<FF>> level_coeffs(level_width);
+        const size_t num_threads = calculate_num_threads(level_width);
+        const size_t range_per_thread = level_width / num_threads;
+        const size_t leftovers = level_width - (range_per_thread * num_threads);
+        parallel_for(num_threads, [&](size_t j) {
+            const size_t offset = j * range_per_thread;
+            const size_t range = (j == num_threads - 1) ? range_per_thread + leftovers : range_per_thread;
+            ASSERT(offset < level_width || level_width == 0);
+            ASSERT((offset + range) <= level_width);
+            for (size_t idx = offset; idx < offset + range; idx++) {
+                // Representing a polynomial of a certain degree requires degree + 1 coefficients
+                level_coeffs[idx].resize(degree + 1);
+            }
+        });
+        return level_coeffs;
+    }
     /**
      * @brief  Recursively compute the parent nodes of each level in the tree, starting from the leaves. Note that at
      * each level, the resulting parent nodes will be polynomials of degree (level+1) because we multiply by an
@@ -171,24 +201,28 @@ template <class DeciderProvingKeys_> class ProtogalaxyProverInternal {
                                                        const std::vector<std::vector<FF>>& prev_level_coeffs,
                                                        size_t level = 1)
     {
+
         if (level == betas.size()) {
             return prev_level_coeffs[0];
         }
-
-        auto degree = level + 1;
-        auto prev_level_width = prev_level_coeffs.size();
-        std::vector<std::vector<FF>> level_coeffs(prev_level_width / 2, std::vector<FF>(degree + 1, 0));
-        parallel_for_heuristic(
-            prev_level_width / 2,
-            [&](size_t parent) {
-                size_t node = parent * 2;
-                std::copy(prev_level_coeffs[node].begin(), prev_level_coeffs[node].end(), level_coeffs[parent].begin());
-                for (size_t d = 0; d < degree; d++) {
-                    level_coeffs[parent][d] += prev_level_coeffs[node + 1][d] * betas[level];
-                    level_coeffs[parent][d + 1] += prev_level_coeffs[node + 1][d] * deltas[level];
-                }
-            },
-            /* overestimate */ thread_heuristics::FF_MULTIPLICATION_COST * degree * 3);
+        const size_t degree = level + 1;
+        const size_t level_width = prev_level_coeffs.size() / 2;
+        std::vector<std::vector<FF>> level_coeffs = initialise_coefficient_tree_level(level_width, degree);
+        {
+            PROFILE_THIS_NAME("other coefficients tree computation");
+            parallel_for_heuristic(
+                level_width,
+                [&](size_t parent) {
+                    size_t node = parent * 2;
+                    std::copy(
+                        prev_level_coeffs[node].begin(), prev_level_coeffs[node].end(), level_coeffs[parent].begin());
+                    for (size_t d = 0; d < degree; d++) {
+                        level_coeffs[parent][d] += prev_level_coeffs[node + 1][d] * betas[level];
+                        level_coeffs[parent][d + 1] += prev_level_coeffs[node + 1][d] * deltas[level];
+                    }
+                },
+                /* overestimate */ thread_heuristics::FF_MULTIPLICATION_COST * degree * 3);
+        }
         return construct_coefficients_tree(betas, deltas, level_coeffs, level + 1);
     }
 
@@ -206,17 +240,21 @@ template <class DeciderProvingKeys_> class ProtogalaxyProverInternal {
                                                               std::span<const FF> deltas,
                                                               const std::vector<FF>& full_honk_evaluations)
     {
-        auto width = full_honk_evaluations.size();
-        std::vector<std::vector<FF>> first_level_coeffs(width / 2, std::vector<FF>(2, 0));
-        parallel_for_heuristic(
-            width / 2,
-            [&](size_t parent) {
-                size_t node = parent * 2;
-                first_level_coeffs[parent][0] =
-                    full_honk_evaluations[node] + full_honk_evaluations[node + 1] * betas[0];
-                first_level_coeffs[parent][1] = full_honk_evaluations[node + 1] * deltas[0];
-            },
-            /* overestimate */ thread_heuristics::FF_MULTIPLICATION_COST * 3);
+
+        const size_t width = full_honk_evaluations.size() / 2;
+        std::vector<std::vector<FF>> first_level_coeffs = initialise_coefficient_tree_level(width, 1);
+        {
+            PROFILE_THIS_NAME("perturbator coefficients first level computation");
+            parallel_for_heuristic(
+                width,
+                [&](size_t parent) {
+                    const size_t node = parent * 2;
+                    first_level_coeffs[parent][0] =
+                        full_honk_evaluations[node] + full_honk_evaluations[node + 1] * betas[0];
+                    first_level_coeffs[parent][1] = full_honk_evaluations[node + 1] * deltas[0];
+                },
+                /* overestimate */ thread_heuristics::FF_MULTIPLICATION_COST * 3);
+        }
         return construct_coefficients_tree(betas, deltas, first_level_coeffs);
     }