diff --git a/lib/test_suite.cpp b/lib/test_suite.cpp
index a77a5ef..b74521f 100644
--- a/lib/test_suite.cpp
+++ b/lib/test_suite.cpp
@@ -41,7 +41,7 @@ void randomized_test(const mealy & specification, const transfer_sequences & pre
 
 	// https://en.wikipedia.org/wiki/Geometric_distribution we have the random variable Y here
 	uniform_int_distribution<> unfair_coin(0, rnd_length);
-	uniform_int_distribution<size_t> prefix_selection(0, prefixes.size() - 1);
+	uniform_int_distribution<state> prefix_selection(0, prefixes.size() - 1);
 	uniform_int_distribution<size_t> suffix_selection;
 	uniform_int_distribution<input> input_selection(0, specification.input_size - 1);
 
diff --git a/lib/transfer_sequences.cpp b/lib/transfer_sequences.cpp
index a459be7..25da8d8 100644
--- a/lib/transfer_sequences.cpp
+++ b/lib/transfer_sequences.cpp
@@ -6,66 +6,38 @@
 #include <numeric>
 #include <queue>
 #include <random>
+#include <tuple>
 
 using namespace std;
 
-transfer_sequences create_transfer_sequences(const mealy& machine, state s){
-	vector<bool> visited(machine.graph_size, false);
-	vector<word> words(machine.graph_size);
-
-	priority_queue<pair<int, state>> work;
-	work.push({0, s});
-	while(!work.empty()){
-		const auto p = work.top();
-		const auto u = p.second;
-		const auto d = p.first - 1;
-		work.pop();
-
-		if(visited[u]) continue;
-
-		visited[u] = true;
-
-		for(input i = 0; i < machine.input_size; ++i){
-			const auto v = apply(machine, u, i).to;
-			if(visited[v]) continue;
-
-			words[v] = words[u];
-			words[v].push_back(i);
-			work.push({d, v});
-		}
-	}
-
-	return words;
-}
-
-transfer_sequences create_randomized_transfer_sequences(const mealy & machine, state s, uint_fast32_t random_seed){
+transfer_sequences create_transfer_sequences(transfer_options const & opt, const mealy & machine,
+                                             state s, uint_fast32_t random_seed) {
 	mt19937 generator(random_seed);
 
-	vector<bool> visited(machine.graph_size, false);
+	vector<bool> added(machine.graph_size, false);
 	vector<word> words(machine.graph_size);
 	vector<input> all_inputs(machine.input_size);
 	iota(begin(all_inputs), end(all_inputs), input(0));
 
-	priority_queue<pair<int, state>> work;
-	work.push({0, s});
-	while(!work.empty()){
-		const auto p = work.top();
-		const auto u = p.second;
-		const auto d = p.first - 1;
+	// state
+	queue<state> work;
+	work.push(s);
+	added[s] = true;
+	while (!work.empty()) {
+		const auto u = work.front();
 		work.pop();
 
-		if(visited[u]) continue;
-
-		visited[u] = true;
-
-		shuffle(begin(all_inputs), end(all_inputs), generator);
-		for(input i : all_inputs){
+		// NOTE: we could also shuffle work, but we would need to do this per distance
+		// the current shuffle is an approximation of real randomization, but easier to implement.
+		if (opt.randomized) shuffle(begin(all_inputs), end(all_inputs), generator);
+		for (input i : all_inputs) {
 			const auto v = apply(machine, u, i).to;
-			if(visited[v]) continue;
+			if (added[v]) continue;
 
+			work.push(v);
+			added[v] = true;
 			words[v] = words[u];
 			words[v].push_back(i);
-			work.push({d, v});
 		}
 	}
 
diff --git a/lib/transfer_sequences.hpp b/lib/transfer_sequences.hpp
index 40bf7f6..285efa3 100644
--- a/lib/transfer_sequences.hpp
+++ b/lib/transfer_sequences.hpp
@@ -4,7 +4,15 @@
 
 struct mealy;
 
+// state -> sequence going to that state
 using transfer_sequences = std::vector<word>;
 
-transfer_sequences create_transfer_sequences(mealy const & machine, state s);
-transfer_sequences create_randomized_transfer_sequences(mealy const & machine, state s, uint_fast32_t random_seed);
+struct transfer_options {
+	bool randomized;
+};
+
+const transfer_options randomized_transfer_sequences{true};
+const transfer_options canonical_transfer_sequences{false};
+
+transfer_sequences create_transfer_sequences(transfer_options const & opt, mealy const & machine,
+                                             state s, uint_fast32_t random_seed);
diff --git a/src/main.cpp b/src/main.cpp
index 7640400..07364fb 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -125,13 +125,11 @@ int main(int argc, char *argv[]) try {
 		return sequence_;
 	}();
 
-	auto transfer_sequences = [&]{
+	auto transfer_sequences = [&] {
 		time_logger t("determining transfer sequences");
-		if(randomize_prefixes){
-			return create_randomized_transfer_sequences(machine, 0, random_seeds[2]);
-		} else {
-			return create_transfer_sequences(machine, 0);
-		}
+		return create_transfer_sequences(randomize_prefixes ? randomized_transfer_sequences
+		                                                    : canonical_transfer_sequences,
+		                                 machine, 0, random_seeds[2]);
 	}();
 
 	auto inputs = create_reverse_map(translation.input_indices);
diff --git a/src/pre_gephi_tool.cpp b/src/pre_gephi_tool.cpp
index d8f46b6..d1e99e5 100644
--- a/src/pre_gephi_tool.cpp
+++ b/src/pre_gephi_tool.cpp
@@ -47,7 +47,7 @@ int main(int argc, char *argv[]){
 	vector<optional<size_t>> visited(machine.graph_size);
 	for(size_t i = 0; i <= maximal_hypothesis; ++i){
 		clog << "Visiting hypo " << i << endl;
-		const auto state_cover = create_transfer_sequences(hypotheses[i], 0);
+		const auto state_cover = create_transfer_sequences(canonical_transfer_sequences, hypotheses[i], 0, 0);
 		for(auto && p : state_cover){
 			state s = 0;
 			for(auto && inp : p){
diff --git a/src/stats.cpp b/src/stats.cpp
index c919386..3289334 100644
--- a/src/stats.cpp
+++ b/src/stats.cpp
@@ -74,7 +74,7 @@ static void print_stats_for_machine(string filename) {
 	const auto reachable_machine = reachable_submachine(machine, 0);
 	cout << '\t' << reachable_machine.graph_size << " reachable states" << endl;
 
-	const auto prefixes = create_transfer_sequences(reachable_machine, 0);
+	const auto prefixes = create_transfer_sequences(canonical_transfer_sequences, reachable_machine, 0, 0);
 	cout << "prefixes ";
 	print_quantiles(prefixes, [](auto const & l) { return l.size(); }, cout);
 	cout << endl;