diff --git a/include/out_of_order_engine.h b/include/out_of_order_engine.h
index 176c3ac47..b60862472 100644
--- a/include/out_of_order_engine.h
+++ b/include/out_of_order_engine.h
@@ -2,6 +2,7 @@
 
 #include <memory>
 #include <optional>
+#include <unordered_set>
 
 namespace celerity::detail::out_of_order_engine_detail {
 struct engine_impl;
@@ -67,6 +68,10 @@ class out_of_order_engine {
 	/// True when all submitted instructions have completed.
 	bool is_idle() const;
 
+	/// Returns the set of all current incomplete instructions that do not have incomplete predecessors themselves, i.e. that are actively executing from the
+	/// out-of-order engine's perspective, not merely eagerly assigned.
+	const std::unordered_set<instruction_id>& get_execution_front() const;
+
 	/// Returns the number of instructions currently awaiting normal or eager assignment (diagnostic use only).
 	size_t get_assignment_queue_length() const;
 
diff --git a/src/live_executor.cc b/src/live_executor.cc
index e01209275..bd410b2e5 100644
--- a/src/live_executor.cc
+++ b/src/live_executor.cc
@@ -313,7 +313,6 @@ struct boundary_check_info {
 
 
 struct async_instruction_state {
-	instruction_id iid = -1;
 	allocation_id alloc_aid = null_allocation_id; ///< non-null iff instruction is an alloc_instruction
 	async_event event;
 	CELERITY_DETAIL_IF_ACCESSOR_BOUNDARY_CHECK(std::unique_ptr<boundary_check_info> oob_info;) // unique_ptr: oob_info is optional and rather large
@@ -331,7 +330,7 @@ struct executor_impl {
 	out_of_order_engine engine{backend->get_system_info()};
 
 	bool expecting_more_submissions = true; ///< shutdown epoch has not been executed yet
-	std::vector<async_instruction_state> in_flight_async_instructions;
+	std::unordered_map<instruction_id, async_instruction_state> in_flight_async_instructions;
 	std::unordered_map<allocation_id, void*> allocations{{null_allocation_id, nullptr}}; ///< obtained from alloc_instruction or track_user_allocation
 	std::unordered_map<host_object_id, std::unique_ptr<host_object_instance>> host_object_instances; ///< passed in through track_host_object_instance
 	std::unordered_map<collective_group_id, std::unique_ptr<communicator>> cloned_communicators;     ///< transitive clones of root_communicator
@@ -350,7 +349,7 @@ struct executor_impl {
 	void poll_in_flight_async_instructions();
 	void poll_submission_queue();
 	void try_issue_one_instruction();
-	void retire_async_instruction(async_instruction_state& async);
+	void retire_async_instruction(instruction_id iid, async_instruction_state& async);
 	void check_progress();
 
 	// Instruction types that complete synchronously within the executor.
@@ -437,12 +436,16 @@ void executor_impl::run() {
 }
 
 void executor_impl::poll_in_flight_async_instructions() {
-	utils::erase_if(in_flight_async_instructions, [&](async_instruction_state& async) {
-		if(!async.event.is_complete()) return false;
-		retire_async_instruction(async);
+	// collect completed instruction ids up-front, since retire_async_instruction would alter the execution front
+	std::vector<instruction_id> completed_now; // std::vector because it will be empty in the common case
+	for(const auto iid : engine.get_execution_front()) {
+		if(in_flight_async_instructions.at(iid).event.is_complete()) { completed_now.push_back(iid); }
+	}
+	for(const auto iid : completed_now) {
+		retire_async_instruction(iid, in_flight_async_instructions.at(iid));
+		in_flight_async_instructions.erase(iid);
 		made_progress = true;
-		return true;
-	});
+	}
 
 	CELERITY_DETAIL_IF_TRACY_ENABLED(tracy->assigned_instructions_plot.update(in_flight_async_instructions.size()));
 }
@@ -478,12 +481,12 @@ void executor_impl::poll_submission_queue() {
 	}
 }
 
-void executor_impl::retire_async_instruction(async_instruction_state& async) {
+void executor_impl::retire_async_instruction(const instruction_id iid, async_instruction_state& async) {
 	CELERITY_DETAIL_TRACY_ZONE_SCOPED("executor::retire", Brown);
 
 #if CELERITY_ACCESSOR_BOUNDARY_CHECK
 	if(async.oob_info != nullptr) {
-		CELERITY_DETAIL_TRACY_ZONE_SCOPED_V("executor::oob_check", Red, "I{} bounds check", async.iid);
+		CELERITY_DETAIL_TRACY_ZONE_SCOPED_V("executor::oob_check", Red, "I{} bounds check", iid);
 		const auto& oob_info = *async.oob_info;
 		for(size_t i = 0; i < oob_info.accessors.size(); ++i) {
 			if(const auto oob_box = oob_info.illegal_access_bounding_boxes[i].into_box(); !oob_box.empty()) {
@@ -502,9 +505,9 @@ void executor_impl::retire_async_instruction(async_instruction_state& async) {
 
 	if(spdlog::should_log(spdlog::level::trace)) {
 		if(const auto native_time = async.event.get_native_execution_time(); native_time.has_value()) {
-			CELERITY_TRACE("[executor] retired I{} after {:.2f}", async.iid, as_sub_second(*native_time));
+			CELERITY_TRACE("[executor] retired I{} after {:.2f}", iid, as_sub_second(*native_time));
 		} else {
-			CELERITY_TRACE("[executor] retired I{}", async.iid);
+			CELERITY_TRACE("[executor] retired I{}", iid);
 		}
 	}
 
@@ -518,7 +521,7 @@ void executor_impl::retire_async_instruction(async_instruction_state& async) {
 		allocations.emplace(async.alloc_aid, ptr);
 	}
 
-	engine.complete_assigned(async.iid);
+	engine.complete_assigned(iid);
 
 	CELERITY_DETAIL_IF_TRACY_ENABLED(tracy->assignment_queue_length_plot.update(engine.get_assignment_queue_length()));
 }
@@ -565,8 +568,7 @@ auto executor_impl::dispatch(const Instr& instr, const out_of_order_engine::assi
 	CELERITY_DETAIL_IF_TRACY_SUPPORTED(tracy_integration::instruction_info info);
 	CELERITY_DETAIL_IF_TRACY_ENABLED(info = tracy_integration::make_instruction_info(instr));
 
-	auto& async = in_flight_async_instructions.emplace_back();
-	async.iid = assignment.instruction->get_id();
+	auto& async = in_flight_async_instructions.emplace(assignment.instruction->get_id(), async_instruction_state{}).first->second;
 	issue_async(instr, assignment, async); // stores event in `async` and completes asynchronously
 	// instr may now dangle
 
@@ -599,9 +601,9 @@ void executor_impl::check_progress() {
 		const auto elapsed_since_last_progress = std::chrono::steady_clock::now() - *last_progress_timestamp;
 		if(elapsed_since_last_progress > *policy.progress_warning_timeout && !progress_warning_emitted) {
 			std::string instr_list;
-			for(auto& in_flight : in_flight_async_instructions) {
+			for(auto& [iid, async] : in_flight_async_instructions) {
 				if(!instr_list.empty()) instr_list += ", ";
-				fmt::format_to(std::back_inserter(instr_list), "I{}", in_flight.iid);
+				fmt::format_to(std::back_inserter(instr_list), "I{}", iid);
 			}
 			CELERITY_WARN("[executor] no progress for {:.0f}, might be stuck. Active instructions: {}", as_sub_second(elapsed_since_last_progress),
 			    in_flight_async_instructions.empty() ? "none" : instr_list);
diff --git a/src/out_of_order_engine.cc b/src/out_of_order_engine.cc
index 5828b081f..c6d0a6344 100644
--- a/src/out_of_order_engine.cc
+++ b/src/out_of_order_engine.cc
@@ -94,6 +94,9 @@ struct engine_impl {
 	/// is assumed to have completed earlier (triggering its removal from the map).
 	std::unordered_map<instruction_id, incomplete_instruction_state> incomplete_instructions;
 
+	/// The subset of assigned, incomplete_instructions that to not have incomplete predecessors themselves.
+	std::unordered_set<instruction_id> execution_front;
+
 	/// Queue of all instructions in `conditional_eagerly_assignable_state` and `unconditional_assignable_state`, in decreasing order of instruction priority.
 	std::priority_queue<const instruction*, std::vector<const instruction*>, instruction_priority_less> assignment_queue;
 
@@ -315,6 +318,8 @@ void engine_impl::complete(const instruction_id iid) {
 	auto deleted_node = std::move(node_it->second); // move so we can access members / iterate successors after erasure
 	incomplete_instructions.erase(node_it);
 
+	execution_front.erase(iid);
+
 	auto& was_assigned = std::get<assigned_state>(deleted_node.assignment);
 	if(deleted_node.target == target::host_queue || deleted_node.target == target::device_queue) {
 		// "remove" instruction from assigned lane
@@ -333,7 +338,11 @@ void engine_impl::complete(const instruction_id iid) {
 			auto& successor = succ_it->second;
 			assert(successor.num_incomplete_predecessors > 0);
 			--successor.num_incomplete_predecessors;
-			try_mark_for_assignment(successor);
+			if(!std::holds_alternative<assigned_state>(successor.assignment)) {
+				try_mark_for_assignment(successor);
+			} else if(successor.num_incomplete_predecessors == 0) {
+				execution_front.insert(succ_iid);
+			}
 		}
 	}
 }
@@ -438,7 +447,9 @@ std::optional<assignment> engine_impl::assign_one() {
 		}
 	}
 
-	return assignment{node.instr, node.target, assigned.device, assigned.lane};
+	if(node.num_incomplete_predecessors == 0) { execution_front.insert(node.instr->get_id()); }
+
+	return assignment(node.instr, node.target, assigned.device, assigned.lane);
 }
 
 } // namespace celerity::detail::out_of_order_engine_detail
@@ -448,6 +459,7 @@ namespace celerity::detail {
 out_of_order_engine::out_of_order_engine(const system_info& system) : m_impl(new out_of_order_engine_detail::engine_impl(system)) {}
 out_of_order_engine::~out_of_order_engine() = default;
 bool out_of_order_engine::is_idle() const { return m_impl->is_idle(); }
+const std::unordered_set<instruction_id>& out_of_order_engine::get_execution_front() const { return m_impl->execution_front; }
 size_t out_of_order_engine::get_assignment_queue_length() const { return m_impl->assignment_queue.size(); }
 void out_of_order_engine::submit(const instruction* const instr) { m_impl->submit(instr); }
 void out_of_order_engine::complete_assigned(const instruction_id iid) { m_impl->complete(iid); }
diff --git a/test/out_of_order_engine_tests.cc b/test/out_of_order_engine_tests.cc
index 147526237..1c0cec985 100644
--- a/test/out_of_order_engine_tests.cc
+++ b/test/out_of_order_engine_tests.cc
@@ -176,6 +176,15 @@ class out_of_order_test_context {
 
 	bool is_idle() const { return m_engine.is_idle(); }
 
+	std::unordered_set<const instruction*> get_execution_front() const {
+		const auto& iid_front = m_engine.get_execution_front();
+		std::unordered_set<const instruction*> instr_front;
+		for(const auto& instr : m_instrs) {
+			if(iid_front.contains(instr->get_id())) { instr_front.insert(instr.get()); }
+		}
+		return instr_front;
+	}
+
   private:
 	instruction_id m_next_iid = 0;
 	std::vector<std::unique_ptr<instruction>> m_instrs;
@@ -203,6 +212,8 @@ TEST_CASE("out_of_order_engine schedules independent chains concurrently", "[out
 	const auto h1 = octx.host_task({h0});
 	const auto h2 = octx.host_task({h0, h1});
 
+	CHECK(octx.get_execution_front().empty());
+
 	{
 		const auto iq = octx.assign_all();
 		CHECK(iq.assigned_instructions_are({d0_k0, d0_k1, d1_k0, d1_k1}));
@@ -215,6 +226,8 @@ TEST_CASE("out_of_order_engine schedules independent chains concurrently", "[out
 		CHECK(iq.assigned_concurrently({d0_k0, d0_k1}, {d1_k0, d1_k1}));
 	}
 
+	CHECK(octx.get_execution_front() == std::unordered_set{d0_k0, d1_k0});
+
 	octx.complete(d0_k0);
 	octx.complete(d0_k1);
 	octx.complete(d1_k0);
@@ -224,13 +237,18 @@ TEST_CASE("out_of_order_engine schedules independent chains concurrently", "[out
 		CHECK(iq.assigned_instructions_are({}));
 	}
 
+	CHECK(octx.get_execution_front() == std::unordered_set{d1_k1});
+
 	octx.complete(d1_k1);
+	CHECK(octx.get_execution_front().empty());
 
 	{
 		const auto iq = octx.assign_all();
 		CHECK(iq.assigned_instructions_are({h0, h1, h2}));
 		CHECK(iq.assigned_in_order({h0, h1, h2}));
 	}
+
+	CHECK(octx.get_execution_front() == std::unordered_set{h0});
 }
 
 TEST_CASE("out_of_order_engine eagerly assigns copy-instructions to the lanes of their dependencies", "[out_of_order_engine]") {
@@ -247,6 +265,8 @@ TEST_CASE("out_of_order_engine eagerly assigns copy-instructions to the lanes of
 
 	CHECK_FALSE(octx.is_idle());
 
+	CHECK(octx.get_execution_front().empty());
+
 	{
 		const auto iq = octx.assign_all();
 		CHECK(iq.assigned_instructions_are({d0_k0, d1_k0, d2_k0, d3_k0, copy_dep0, copy_dep1, copy_dep2, copy_dep3}));
@@ -260,11 +280,18 @@ TEST_CASE("out_of_order_engine eagerly assigns copy-instructions to the lanes of
 		CHECK(iq.assigned_in_order({d3_k0, copy_dep3}));
 	}
 
+	CHECK(octx.get_execution_front() == std::unordered_set{d0_k0, d1_k0, d2_k0, d3_k0});
+
 	octx.complete(d0_k0);
 	octx.complete(d1_k0);
+
+	CHECK(octx.get_execution_front() == std::unordered_set{d2_k0, d3_k0, copy_dep0, copy_dep1});
+
 	octx.complete(d2_k0);
 	octx.complete(d3_k0);
+
 	CHECK_FALSE(octx.is_idle());
+	CHECK(octx.get_execution_front() == std::unordered_set{copy_dep0, copy_dep1, copy_dep2, copy_dep3});
 
 	const auto copy_indep0 = octx.copy({d0_k0 /* already complete */}, first_device_memory_id + 1, first_device_memory_id);
 	const auto copy_indep1 = octx.copy({d1_k0 /* already complete */}, first_device_memory_id, first_device_memory_id + 1);
@@ -361,17 +388,23 @@ TEST_CASE("out_of_order_engine does not attempt to assign instructions more than
 	out_of_order_test_context octx(1);
 	auto k1 = octx.device_kernel({}, device_id(0));
 	auto k2 = octx.device_kernel({k1}, device_id(0));
+	CHECK(octx.get_execution_front().empty());
 
 	const auto assigned = octx.assign_one();
 	REQUIRE(assigned.has_value());
 	CHECK(assigned->instruction == k1);
+	CHECK(octx.get_execution_front() == std::unordered_set{k1});
 
 	octx.complete(k1);
 
+	CHECK(octx.get_execution_front().empty());
+
 	const auto other = octx.assign_all();
 	CHECK(other.assigned_instructions_are({k2}));
+	CHECK(octx.get_execution_front() == std::unordered_set{k2});
 
 	octx.complete(k2);
+	CHECK(octx.get_execution_front().empty());
 	CHECK(octx.is_idle());
 }
 
@@ -381,15 +414,19 @@ TEST_CASE("assigned sets of instructions with internal dependencies can be compl
 	out_of_order_test_context octx(1);
 	auto k1 = octx.device_kernel({}, device_id(0));
 	auto k2 = octx.device_kernel({k1}, device_id(0));
+	CHECK(octx.get_execution_front().empty());
 
 	octx.assign_all();
 	CHECK_FALSE(octx.is_idle());
+	CHECK(octx.get_execution_front() == std::unordered_set{k1});
 
 	octx.complete(k2);
 	CHECK_FALSE(octx.is_idle());
+	CHECK(octx.get_execution_front() == std::unordered_set{k1});
 
 	octx.complete(k1);
 	CHECK(octx.is_idle());
+	CHECK(octx.get_execution_front().empty());
 }
 
 TEST_CASE("concurrent instructions are assigned in decreasing priority", "[out_of_order_engine]") {