diff --git a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.cpp b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.cpp
index 372926ddafb..b32aecff411 100644
--- a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.cpp
+++ b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.cpp
@@ -154,17 +154,9 @@ template <class ProverInstances> void ProtoGalaxyProver_<ProverInstances>::prepa
         send_accumulator(instance, domain_separator);
     } else {
         // This is the first round of folding and we need to generate some gate challenges.
-        // TODO(https://github.com/AztecProtocol/barretenberg/issues/740): implement option 2 to make this more
-        // efficient by avoiding the computation of the perturbator
         finalise_and_send_instance(instance, domain_separator);
         instance->target_sum = 0;
-        auto beta = transcript->template get_challenge<FF>(domain_separator + "_initial_gate_challenge");
-        std::vector<FF> gate_challenges(instance->log_instance_size);
-        gate_challenges[0] = beta;
-        for (size_t i = 1; i < instance->log_instance_size; i++) {
-            gate_challenges[i] = gate_challenges[i - 1].sqr();
-        }
-        instance->gate_challenges = gate_challenges;
+        instance->gate_challenges = std::vector<FF>(instance->log_instance_size, 0);
     }
 
     idx++;
@@ -315,9 +307,13 @@ template <class ProverInstances> void ProtoGalaxyProver_<ProverInstances>::pertu
     state.accumulator = get_accumulator();
     FF delta = transcript->template get_challenge<FF>("delta");
     state.deltas = compute_round_challenge_pows(state.accumulator->log_instance_size, delta);
-    state.perturbator = compute_perturbator(state.accumulator, state.deltas);
-    for (size_t idx = 0; idx <= state.accumulator->log_instance_size; idx++) {
-        transcript->send_to_verifier("perturbator_" + std::to_string(idx), state.perturbator[idx]);
+    state.perturbator = Polynomial<FF>(state.accumulator->log_instance_size + 1); // initialize to all zeros
+    // compute perturbator only if this is not the first round and has an accumulator
+    if (state.accumulator->is_accumulator) {
+        state.perturbator = compute_perturbator(state.accumulator, state.deltas);
+        for (size_t idx = 0; idx <= state.accumulator->log_instance_size; idx++) {
+            transcript->send_to_verifier("perturbator_" + std::to_string(idx), state.perturbator[idx]);
+        }
     }
 };
 
diff --git a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp
index cbe139eb37c..0df61d1d82f 100644
--- a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp
+++ b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_prover.hpp
@@ -134,8 +134,6 @@ template <class ProverInstances_> class ProtoGalaxyProver_ {
 
     // Returns the accumulator, which is the first element in ProverInstances. The accumulator is assumed to have the
     // FoldingParameters set and be the result of a previous round of folding.
-    // TODO(https://github.com/AztecProtocol/barretenberg/issues/740): handle the case when the accumulator is empty
-    // (i.e. we are in the first round of folding)/
     std::shared_ptr<Instance> get_accumulator() { return instances[0]; }
 
     /**
diff --git a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_verifier.cpp b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_verifier.cpp
index 07b32554f34..bdcfa0500e9 100644
--- a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_verifier.cpp
+++ b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_verifier.cpp
@@ -159,17 +159,9 @@ void ProtoGalaxyVerifier_<VerifierInstances>::prepare_for_folding(const std::vec
         receive_accumulator(inst, domain_separator);
     } else {
         // This is the first round of folding and we need to generate some gate challenges.
-        // TODO(https://github.com/AztecProtocol/barretenberg/issues/740): implement option 2 to make this more
-        // efficient by avoiding the computation of the perturbator
         receive_and_finalise_instance(inst, domain_separator);
         inst->target_sum = 0;
-        auto beta = transcript->template get_challenge<FF>(domain_separator + "_initial_gate_challenge");
-        std::vector<FF> gate_challenges(inst->log_instance_size);
-        gate_challenges[0] = beta;
-        for (size_t i = 1; i < inst->log_instance_size; i++) {
-            gate_challenges[i] = gate_challenges[i - 1].sqr();
-        }
-        inst->gate_challenges = gate_challenges;
+        inst->gate_challenges = std::vector<FF>(inst->log_instance_size, 0);
     }
     index++;
 
@@ -189,9 +181,12 @@ bool ProtoGalaxyVerifier_<VerifierInstances>::verify_folding_proof(const std::ve
     auto accumulator = get_accumulator();
     auto deltas = compute_round_challenge_pows(accumulator->log_instance_size, delta);
 
-    std::vector<FF> perturbator_coeffs(accumulator->log_instance_size + 1);
-    for (size_t idx = 0; idx <= accumulator->log_instance_size; idx++) {
-        perturbator_coeffs[idx] = transcript->template receive_from_prover<FF>("perturbator_" + std::to_string(idx));
+    std::vector<FF> perturbator_coeffs(accumulator->log_instance_size + 1, 0);
+    if (accumulator->is_accumulator) {
+        for (size_t idx = 0; idx <= accumulator->log_instance_size; idx++) {
+            perturbator_coeffs[idx] =
+                transcript->template receive_from_prover<FF>("perturbator_" + std::to_string(idx));
+        }
     }
 
     if (perturbator_coeffs[0] != accumulator->target_sum) {
diff --git a/barretenberg/cpp/src/barretenberg/stdlib/recursion/honk/verifier/protogalaxy_recursive_verifier.cpp b/barretenberg/cpp/src/barretenberg/stdlib/recursion/honk/verifier/protogalaxy_recursive_verifier.cpp
index 047cfa4037e..6ac10f7cd30 100644
--- a/barretenberg/cpp/src/barretenberg/stdlib/recursion/honk/verifier/protogalaxy_recursive_verifier.cpp
+++ b/barretenberg/cpp/src/barretenberg/stdlib/recursion/honk/verifier/protogalaxy_recursive_verifier.cpp
@@ -164,17 +164,9 @@ template <class VerifierInstances> void ProtoGalaxyRecursiveVerifier_<VerifierIn
         receive_accumulator(inst, domain_separator);
     } else {
         // This is the first round of folding and we need to generate some gate challenges.
-        // TODO(https://github.com/AztecProtocol/barretenberg/issues/740): implement option 2 to make this more
-        // efficient by avoiding the computation of the perturbator
         receive_and_finalise_instance(inst, domain_separator);
         inst->target_sum = 0;
-        auto beta = transcript->template get_challenge<FF>(domain_separator + "_initial_gate_challenge");
-        std::vector<FF> gate_challenges(inst->log_instance_size);
-        gate_challenges[0] = beta;
-        for (size_t i = 1; i < inst->log_instance_size; i++) {
-            gate_challenges[i] = gate_challenges[i - 1].sqr();
-        }
-        inst->gate_challenges = gate_challenges;
+        inst->gate_challenges = std::vector<FF>(inst->log_instance_size, 0);
     }
     index++;
 
@@ -199,9 +191,12 @@ void ProtoGalaxyRecursiveVerifier_<VerifierInstances>::verify_folding_proof(cons
     auto accumulator = get_accumulator();
     auto deltas = compute_round_challenge_pows(accumulator->log_instance_size, delta);
 
-    std::vector<FF> perturbator_coeffs(accumulator->log_instance_size + 1);
-    for (size_t idx = 0; idx <= accumulator->log_instance_size; idx++) {
-        perturbator_coeffs[idx] = transcript->template receive_from_prover<FF>("perturbator_" + std::to_string(idx));
+    std::vector<FF> perturbator_coeffs(accumulator->log_instance_size + 1, 0);
+    if (accumulator->is_accumulator) {
+        for (size_t idx = 0; idx <= accumulator->log_instance_size; idx++) {
+            perturbator_coeffs[idx] =
+                transcript->template receive_from_prover<FF>("perturbator_" + std::to_string(idx));
+        }
     }
 
     // TODO(https://github.com/AztecProtocol/barretenberg/issues/833): As currently the stdlib transcript is not