diff --git a/backends/aiger/xaiger.cc b/backends/aiger/xaiger.cc
index 97fec9376..9e5d44470 100644
--- a/backends/aiger/xaiger.cc
+++ b/backends/aiger/xaiger.cc
@@ -174,6 +174,7 @@ struct XAigerWriter
 					if (bit != wirebit)
 						alias_map[bit] = wirebit;
 					input_bits.insert(wirebit);
+					undriven_bits.erase(bit);
 				}
 
 				if (wire->port_output || keep) {
@@ -181,6 +182,8 @@ struct XAigerWriter
 						if (bit != wirebit)
 							alias_map[wirebit] = bit;
 						output_bits.insert(wirebit);
+						if (!wire->port_input)
+							unused_bits.erase(bit);
 					}
 					else
 						log_debug("Skipping PO '%s' driven by 1'bx\n", log_signal(wirebit));
@@ -188,12 +191,6 @@ struct XAigerWriter
 			}
 		}
 
-		for (auto bit : input_bits)
-			undriven_bits.erase(sigmap(bit));
-		for (auto bit : output_bits)
-			if (!bit.wire->port_input)
-				unused_bits.erase(bit);
-
 		// TODO: Speed up toposort -- ultimately we care about
 		//       box ordering, but not individual AIG cells
 		dict<SigBit, pool<IdString>> bit_drivers, bit_users;