diff --git a/passes/techmap/flowmap.cc b/passes/techmap/flowmap.cc
index 5807178dd..a2ad87f7d 100644
--- a/passes/techmap/flowmap.cc
+++ b/passes/techmap/flowmap.cc
@@ -394,7 +394,7 @@ struct FlowGraph
 
 	pair<pool<RTLIL::SigBit>, pool<RTLIL::SigBit>> edge_cut()
 	{
-		pool<RTLIL::SigBit> x, xi;
+		pool<RTLIL::SigBit> x = {source}, xi; // X and X̅ in the paper
 
 		NodePrime source_prime = {source, true};
 		pool<NodePrime> visited;
@@ -437,6 +437,7 @@ struct FlowGraph
 		for (auto collapsed_node : collapsed[sink])
 			xi.insert(collapsed_node);
 
+		log_assert(x[source] && !xi[source]);
 		log_assert(!x[sink] && xi[sink]);
 		return {x, xi};
 	}
@@ -1050,7 +1051,7 @@ struct FlowmapWorker
 
 				auto cut_inputs = cut_lut_at_gate(lut, lut_gate);
 				pool<RTLIL::SigBit> gate_inputs = cut_inputs.first, other_inputs = cut_inputs.second;
-				if (gate_inputs.empty() && (int)other_inputs.size() == order)
+				if (gate_inputs.empty() && (int)other_inputs.size() >= order)
 				{
 					if (debug_relax)
 						log("      Breaking would result in a (k+1)-LUT.\n");