diff --git a/barretenberg/cpp/src/barretenberg/flavor/flavor.hpp b/barretenberg/cpp/src/barretenberg/flavor/flavor.hpp
index d2a847a0dbc..6be12a498ff 100644
--- a/barretenberg/cpp/src/barretenberg/flavor/flavor.hpp
+++ b/barretenberg/cpp/src/barretenberg/flavor/flavor.hpp
@@ -241,6 +241,26 @@ static constexpr auto create_protogalaxy_tuple_of_tuples_of_univariates()
     }
 }
 
+/**
+ * @brief Recursive utility function to construct a container for the subrelation accumulators of Protogalaxy folding.
+ * @details The size of the outer tuple is equal to the number of relations. Each relation contributes an inner tuple of
+ * univariates whose size is equal to the number of subrelations of the relation. The length of a univariate in an inner
+ * tuple is determined by the corresponding subrelation length and the number of instances to be folded.
+ */
+template <typename Tuple, size_t NUM_INSTANCES, size_t Index = 0>
+static constexpr auto create_optimised_protogalaxy_tuple_of_tuples_of_univariates()
+{
+    if constexpr (Index >= std::tuple_size<Tuple>::value) {
+        return std::tuple<>{}; // Return empty when reach end of the tuple
+    } else {
+        using UnivariateTuple = typename std::tuple_element_t<Index, Tuple>::
+            template OptimisedProtogalaxyTupleOfUnivariatesOverSubrelations<NUM_INSTANCES>;
+        return std::tuple_cat(
+            std::tuple<UnivariateTuple>{},
+            create_optimised_protogalaxy_tuple_of_tuples_of_univariates<Tuple, NUM_INSTANCES, Index + 1>());
+    }
+}
+
 /**
  * @brief Recursive utility function to construct a container for the subrelation accumulators of sumcheck proving.
  * @details The size of the outer tuple is equal to the number of relations. Each relation contributes an inner tuple of
diff --git a/barretenberg/cpp/src/barretenberg/polynomials/univariate.hpp b/barretenberg/cpp/src/barretenberg/polynomials/univariate.hpp
index aedc1353787..943f9be4201 100644
--- a/barretenberg/cpp/src/barretenberg/polynomials/univariate.hpp
+++ b/barretenberg/cpp/src/barretenberg/polynomials/univariate.hpp
@@ -271,7 +271,7 @@ template <class Fr, size_t domain_end, size_t domain_start = 0> class Univariate
      * subtraction: setting Δ = v1-v0, the values of f(X) are f(0)=v0, f(1)= v0 + Δ, v2 = f(1) + Δ, v3 = f(2) + Δ...
      *
      */
-    template <size_t EXTENDED_DOMAIN_END> Univariate<Fr, EXTENDED_DOMAIN_END> extend_to() const
+    template <size_t EXTENDED_DOMAIN_END, bool optimised = false> Univariate<Fr, EXTENDED_DOMAIN_END> extend_to() const
     {
         const size_t EXTENDED_LENGTH = EXTENDED_DOMAIN_END - domain_start;
         using Data = BarycentricData<Fr, LENGTH, EXTENDED_LENGTH>;
@@ -282,11 +282,20 @@ template <class Fr, size_t domain_end, size_t domain_start = 0> class Univariate
         std::copy(evaluations.begin(), evaluations.end(), result.evaluations.begin());
 
         static constexpr Fr inverse_two = Fr(2).invert();
+        // static_assert(!optimised || (LENGTH <= 2));
         if constexpr (LENGTH == 2) {
             Fr delta = value_at(1) - value_at(0);
             static_assert(EXTENDED_LENGTH != 0);
-            for (size_t idx = domain_end - 1; idx < EXTENDED_DOMAIN_END - 1; idx++) {
-                result.value_at(idx + 1) = result.value_at(idx) + delta;
+            if constexpr (optimised) {
+                Fr current = result.value_at(1);
+                for (size_t idx = domain_end - 2; idx < EXTENDED_DOMAIN_END - 1; idx++) {
+                    current += delta;
+                    result.value_at(idx + 1) = current;
+                }
+            } else {
+                for (size_t idx = domain_end - 1; idx < EXTENDED_DOMAIN_END - 1; idx++) {
+                    result.value_at(idx + 1) = result.value_at(idx) + delta;
+                }
             }
             return result;
         } else if constexpr (LENGTH == 3) {
diff --git a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp
index ee3fd0c08d0..423cd67afda 100644
--- a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp
+++ b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp
@@ -49,15 +49,21 @@ template <class ProverInstances_> class ProtoGalaxyProver_ {
     // The length of ExtendedUnivariate is the largest length (==max_relation_degree + 1) of a univariate polynomial
     // obtained by composing a relation with folded instance + relation parameters .
     using ExtendedUnivariate = Univariate<FF, (Flavor::MAX_TOTAL_RELATION_LENGTH - 1) * (ProverInstances::NUM - 1) + 1>;
+    using OptimisedExtendedUnivariate =
+        Univariate<FF, (Flavor::MAX_TOTAL_RELATION_LENGTH - 2) * (ProverInstances::NUM - 1) + 1>;
     // Represents the total length of the combiner univariate, obtained by combining the already folded relations with
     // the folded relation batching challenge.
     using ExtendedUnivariateWithRandomization =
         Univariate<FF,
                    (Flavor::MAX_TOTAL_RELATION_LENGTH - 1 + ProverInstances::NUM - 1) * (ProverInstances::NUM - 1) + 1>;
     using ExtendedUnivariates = typename Flavor::template ProverUnivariates<ExtendedUnivariate::LENGTH>;
+    using OptimisedExtendedUnivariates =
+        typename Flavor::template ProverUnivariates<ExtendedUnivariate::LENGTH - (1 * (ProverInstances::NUM - 1))>;
 
     using TupleOfTuplesOfUnivariates =
         typename Flavor::template ProtogalaxyTupleOfTuplesOfUnivariates<ProverInstances::NUM>;
+    using OptimisedTupleOfTuplesOfUnivariates =
+        typename Flavor::template OptimisedProtogalaxyTupleOfTuplesOfUnivariates<ProverInstances::NUM>;
     using RelationEvaluations = typename Flavor::TupleOfArraysOfValues;
 
     static constexpr size_t NUM_SUBRELATIONS = ProverInstances::NUM_SUBRELATIONS;
@@ -291,9 +297,27 @@ template <class ProverInstances_> class ProtoGalaxyProver_ {
         }
     }
 
+    /**
+     * @brief Prepare a univariate polynomial for relation execution in one step of the main loop in folded instance
+     * construction.
+     * @details For a fixed prover polynomial index, extract that polynomial from each instance in Instances. From each
+     * polynomial, extract the value at row_idx. Use these values to create a univariate polynomial, and then extend
+     * (i.e., compute additional evaluations at adjacent domain values) as needed.
+     * @todo TODO(https://github.com/AztecProtocol/barretenberg/issues/751) Optimize memory
+     */
+    void optimised_extend_univariates(OptimisedExtendedUnivariates& extended_univariates,
+                                      const ProverInstances& instances,
+                                      const size_t row_idx)
+    {
+        auto base_univariates = instances.row_to_univariates(row_idx);
+        for (auto [extended_univariate, base_univariate] : zip_view(extended_univariates.get_all(), base_univariates)) {
+            extended_univariate = base_univariate.template extend_to<OptimisedExtendedUnivariate::LENGTH, true>();
+        }
+    }
+
     template <typename Parameters, size_t relation_idx = 0>
-    void accumulate_relation_univariates(TupleOfTuplesOfUnivariates& univariate_accumulators,
-                                         const ExtendedUnivariates& extended_univariates,
+    void accumulate_relation_univariates(OptimisedTupleOfTuplesOfUnivariates& univariate_accumulators,
+                                         const OptimisedExtendedUnivariates& extended_univariates,
                                          const Parameters& relation_parameters,
                                          const FF& scaling_factor)
     {
@@ -329,14 +353,14 @@ template <class ProverInstances_> class ProtoGalaxyProver_ {
         num_threads = num_threads > 0 ? num_threads : 1;                     // ensure num threads is >= 1
         size_t iterations_per_thread = common_instance_size / num_threads;   // actual iterations per thread
         // Construct univariate accumulator containers; one per thread
-        std::vector<TupleOfTuplesOfUnivariates> thread_univariate_accumulators(num_threads);
+        std::vector<OptimisedTupleOfTuplesOfUnivariates> thread_univariate_accumulators(num_threads);
         for (auto& accum : thread_univariate_accumulators) {
             // just normal relation lengths
             Utils::zero_univariates(accum);
         }
 
         // Construct extended univariates containers; one per thread
-        std::vector<ExtendedUnivariates> extended_univariates;
+        std::vector<OptimisedExtendedUnivariates> extended_univariates;
         extended_univariates.resize(num_threads);
 
         // Accumulate the contribution from each sub-relation
@@ -346,7 +370,7 @@ template <class ProverInstances_> class ProtoGalaxyProver_ {
 
             for (size_t idx = start; idx < end; idx++) {
                 // No need to initialise extended_univariates to 0, it's assigned to
-                extend_univariates(extended_univariates[thread_idx], instances, idx);
+                optimised_extend_univariates(extended_univariates[thread_idx], instances, idx);
 
                 FF pow_challenge = pow_betas[idx];
 
@@ -360,15 +384,36 @@ template <class ProverInstances_> class ProtoGalaxyProver_ {
                     pow_challenge);
             }
         });
-
+        OptimisedTupleOfTuplesOfUnivariates optimised_univariate_accumulators;
+        Utils::zero_univariates(optimised_univariate_accumulators);
         // Accumulate the per-thread univariate accumulators into a single set of accumulators
         for (auto& accumulators : thread_univariate_accumulators) {
-            Utils::add_nested_tuples(univariate_accumulators, accumulators);
+            Utils::add_nested_tuples(optimised_univariate_accumulators, accumulators);
         }
+        deoptimise_univariates(optimised_univariate_accumulators, univariate_accumulators);
         // Batch the univariate contributions from each sub-relation to obtain the round univariate
         return batch_over_relations(univariate_accumulators, instances.alphas);
     }
 
+    static void deoptimise_univariates(OptimisedTupleOfTuplesOfUnivariates& optimised_univariate_accumulators,
+                                       TupleOfTuplesOfUnivariates& univariate_accumulators
+
+    )
+    {
+        auto deoptimise = [&]<size_t outer_idx, size_t inner_idx>(auto& element) {
+            auto& optimised_element = std::get<inner_idx>(std::get<outer_idx>(optimised_univariate_accumulators));
+            static_assert(std::remove_reference_t<decltype(optimised_element)>::LENGTH + (ProverInstances::NUM - 1) ==
+                          std::remove_reference_t<decltype(element)>::LENGTH);
+            element.evaluations[0] = optimised_element.evaluations[0];
+            element.evaluations[1] = FF(0);
+            for (size_t i = 1; i < std::remove_reference_t<decltype(optimised_element)>::LENGTH; i++) {
+                element.evaluations[i + 1] = optimised_element.evaluations[i];
+            }
+        };
+
+        Utils::template apply_to_tuple_of_tuples<0, 0>(univariate_accumulators, deoptimise);
+    }
+
     static ExtendedUnivariateWithRandomization batch_over_relations(TupleOfTuplesOfUnivariates& univariate_accumulators,
                                                                     const CombinedRelationSeparator& alpha)
     {
@@ -378,6 +423,7 @@ template <class ProverInstances_> class ProtoGalaxyProver_ {
         size_t idx = 0;
         auto scale_and_sum = [&]<size_t outer_idx, size_t inner_idx>(auto& element) {
             auto extended = element.template extend_to<ProverInstances::BATCHED_EXTENDED_LENGTH>();
+            // info("Relation ", outer_idx, ".", inner_idx, "[", 0, "] = ", extended.value_at(0));
             extended *= alpha[idx];
             result += extended;
             idx++;
diff --git a/barretenberg/cpp/src/barretenberg/relations/relation_types.hpp b/barretenberg/cpp/src/barretenberg/relations/relation_types.hpp
index be4b8732254..19bc2f0e79c 100644
--- a/barretenberg/cpp/src/barretenberg/relations/relation_types.hpp
+++ b/barretenberg/cpp/src/barretenberg/relations/relation_types.hpp
@@ -89,6 +89,28 @@ consteval std::array<size_t, NUM_SUBRELATIONS> compute_composed_subrelation_part
     return SUBRELATION_PARTIAL_LENGTHS;
 };
 
+/**
+ * @brief Get the subrelation accumulators for the Protogalaxy combiner calculation.
+ * @details A subrelation of degree D, when evaluated on polynomials of degree N, gives a polynomial of degree D
+ * * N. In the context of Protogalaxy, N = NUM_INSTANCES-1. Hence, given a subrelation of length x, its
+ * evaluation on such polynomials will have degree (x-1) * (NUM_INSTANCES-1), and the length of this evaluation
+ * will be one greater than this.
+ * @tparam NUM_INSTANCES
+ * @tparam NUM_SUBRELATIONS
+ * @param SUBRELATION_PARTIAL_LENGTHS The array of subrelation lengths supplied by a relation.
+ * @return The transformed subrelation lenths
+ */
+template <size_t NUM_INSTANCES, size_t NUM_SUBRELATIONS>
+consteval std::array<size_t, NUM_SUBRELATIONS> compute_optimised_composed_subrelation_partial_lengths(
+    std::array<size_t, NUM_SUBRELATIONS> SUBRELATION_PARTIAL_LENGTHS)
+{
+    std::transform(SUBRELATION_PARTIAL_LENGTHS.begin(),
+                   SUBRELATION_PARTIAL_LENGTHS.end(),
+                   SUBRELATION_PARTIAL_LENGTHS.begin(),
+                   [](const size_t x) { return (x - 2) * (NUM_INSTANCES - 1) + 1; });
+    return SUBRELATION_PARTIAL_LENGTHS;
+};
+
 /**
  * @brief The templates defined herein facilitate sharing the relation arithmetic between the prover and the
  * verifier.
@@ -134,6 +156,11 @@ template <typename RelationImpl> class Relation : public RelationImpl {
     template <size_t NUM_INSTANCES>
     using ProtogalaxyTupleOfUnivariatesOverSubrelations =
         TupleOfUnivariates<FF, compute_composed_subrelation_partial_lengths<NUM_INSTANCES>(SUBRELATION_TOTAL_LENGTHS)>;
+    template <size_t NUM_INSTANCES>
+    using OptimisedProtogalaxyTupleOfUnivariatesOverSubrelations =
+        TupleOfUnivariates<FF,
+                           compute_optimised_composed_subrelation_partial_lengths<NUM_INSTANCES>(
+                               SUBRELATION_TOTAL_LENGTHS)>;
     using SumcheckTupleOfUnivariatesOverSubrelations =
         TupleOfUnivariates<FF, RelationImpl::SUBRELATION_PARTIAL_LENGTHS>;
     using SumcheckArrayOfValuesOverSubrelations = ArrayOfValues<FF, RelationImpl::SUBRELATION_PARTIAL_LENGTHS>;
diff --git a/barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/goblin_ultra_flavor.hpp b/barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/goblin_ultra_flavor.hpp
index 677749016b5..d5f4b8a2c4e 100644
--- a/barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/goblin_ultra_flavor.hpp
+++ b/barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/goblin_ultra_flavor.hpp
@@ -87,6 +87,10 @@ class GoblinUltraFlavor {
     template <size_t NUM_INSTANCES>
     using ProtogalaxyTupleOfTuplesOfUnivariates =
         decltype(create_protogalaxy_tuple_of_tuples_of_univariates<Relations, NUM_INSTANCES>());
+
+    template <size_t NUM_INSTANCES>
+    using OptimisedProtogalaxyTupleOfTuplesOfUnivariates =
+        decltype(create_optimised_protogalaxy_tuple_of_tuples_of_univariates<Relations, NUM_INSTANCES>());
     using SumcheckTupleOfTuplesOfUnivariates = decltype(create_sumcheck_tuple_of_tuples_of_univariates<Relations>());
     using TupleOfArraysOfValues = decltype(create_tuple_of_arrays_of_values<Relations>());
 
diff --git a/barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/ultra_flavor.hpp b/barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/ultra_flavor.hpp
index bb40fe0c7ff..618dedcecb3 100644
--- a/barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/ultra_flavor.hpp
+++ b/barretenberg/cpp/src/barretenberg/stdlib_circuit_builders/ultra_flavor.hpp
@@ -75,6 +75,9 @@ class UltraFlavor {
     template <size_t NUM_INSTANCES>
     using ProtogalaxyTupleOfTuplesOfUnivariates =
         decltype(create_protogalaxy_tuple_of_tuples_of_univariates<Relations, NUM_INSTANCES>());
+    template <size_t NUM_INSTANCES>
+    using OptimisedProtogalaxyTupleOfTuplesOfUnivariates =
+        decltype(create_optimised_protogalaxy_tuple_of_tuples_of_univariates<Relations, NUM_INSTANCES>());
     using SumcheckTupleOfTuplesOfUnivariates = decltype(create_sumcheck_tuple_of_tuples_of_univariates<Relations>());
     using TupleOfArraysOfValues = decltype(create_tuple_of_arrays_of_values<Relations>());
 
diff --git a/barretenberg/cpp/src/barretenberg/vm/generated/avm_flavor.hpp b/barretenberg/cpp/src/barretenberg/vm/generated/avm_flavor.hpp
index 4bb786ea4cb..1bc1245b2f1 100644
--- a/barretenberg/cpp/src/barretenberg/vm/generated/avm_flavor.hpp
+++ b/barretenberg/cpp/src/barretenberg/vm/generated/avm_flavor.hpp
@@ -154,6 +154,9 @@ class AvmFlavor {
     template <size_t NUM_INSTANCES>
     using ProtogalaxyTupleOfTuplesOfUnivariates =
         decltype(create_protogalaxy_tuple_of_tuples_of_univariates<Relations, NUM_INSTANCES>());
+    template <size_t NUM_INSTANCES>
+    using OptimisedProtogalaxyTupleOfTuplesOfUnivariates =
+        decltype(create_optimised_protogalaxy_tuple_of_tuples_of_univariates<Relations, NUM_INSTANCES>());
     using SumcheckTupleOfTuplesOfUnivariates = decltype(create_sumcheck_tuple_of_tuples_of_univariates<Relations>());
     using TupleOfArraysOfValues = decltype(create_tuple_of_arrays_of_values<Relations>());