diff --git a/tket2-hseries/src/lazify_measure.rs b/tket2-hseries/src/lazify_measure.rs
index e1e0c2f5..7a233ced 100644
--- a/tket2-hseries/src/lazify_measure.rs
+++ b/tket2-hseries/src/lazify_measure.rs
@@ -125,7 +125,10 @@ impl LazifyMeasureRewrite {
         Self::check_signature(node, QSystemOp::LazyMeasure, hugr.get_optype(node))?;
 
         let subgraph = SiblingSubgraph::from_node(node, &hugr);
-        let uses = hugr.linked_inputs(node, 0).collect_vec();
+        // SimpleReplacement adds edges in a nondeterministic order.  This
+        // results in linked_inputs returning items in a nondeterministic
+        // order. We sort them here to restore determinism.
+        let uses = hugr.linked_inputs(node, 0).sorted().collect_vec();
         let (lazy_measure_node, replacement) = {
             let bool_uses = uses.len();
             let mut builder =
@@ -165,7 +168,8 @@ impl LazifyMeasureRewrite {
         Self::check_signature(node, QSystemOp::LazyMeasureReset, hugr.get_optype(node))?;
 
         let subgraph = SiblingSubgraph::from_node(node, &hugr);
-        let uses = hugr.linked_inputs(node, 1).collect_vec();
+        // See comment in try_new_measure
+        let uses = hugr.linked_inputs(node, 1).sorted().collect_vec();
         let (lazy_measure_reset_node, replacement) = {
             let bool_uses = uses.len();
             let mut builder = {