diff --git a/cpp/ql/src/Critical/NewDelete.qll b/cpp/ql/src/Critical/NewDelete.qll
index 05c641c04c32..97848e3bbdf2 100644
--- a/cpp/ql/src/Critical/NewDelete.qll
+++ b/cpp/ql/src/Critical/NewDelete.qll
@@ -46,32 +46,20 @@ predicate allocExprOrIndirect(Expr alloc, string kind) {
     alloc.(FunctionCall).getTarget() = rtn.getEnclosingFunction() and
     (
       allocExprOrIndirect(rtn.getExpr(), kind) or
-      allocReaches(rtn.getExpr(), _, kind)
+      allocReaches0(rtn.getExpr(), _, kind)
     )
   )
 }
 
 /**
- * Holds if `v` is assigned value `e`, and `e` is not known to be `0`.
+ * Holds if `v` is a non-local variable which is assigned with allocations of
+ * type `kind`.
  */
-private predicate nonNullGlobalAssignment(Variable v, Expr e) {
-  not v instanceof LocalScopeVariable and
-  v.getAnAssignedValue() = e and
-  not e.getValue().toInt() = 0
-}
-
-/**
- * Holds if `v` is a non-local variable which is assigned only with allocations of
- * type `kind` (it may also be assigned with NULL).
- */
-private predicate allocReachesVariable(Variable v, Expr alloc, string kind) {
+private pragma[nomagic] predicate allocReachesVariable(Variable v, Expr alloc, string kind) {
   exists(Expr mid |
-    nonNullGlobalAssignment(v, mid) and
-    allocReaches(mid, alloc, kind)
-  ) and
-  forall(Expr mid |
-    nonNullGlobalAssignment(v, mid) |
-    allocReaches(mid, _, kind)
+    not v instanceof LocalScopeVariable and
+    v.getAnAssignedValue() = mid and
+    allocReaches0(mid, alloc, kind)
   )
 }
 
@@ -80,22 +68,35 @@ private predicate allocReachesVariable(Variable v, Expr alloc, string kind) {
  * result of a previous memory allocation `alloc`.  `kind` is a
  * string describing the type of that allocation.
  */
-predicate allocReaches(Expr e, Expr alloc, string kind) {
+private predicate allocReaches0(Expr e, Expr alloc, string kind) {
   (
     // alloc
     allocExprOrIndirect(alloc, kind) and
     e = alloc
   ) or exists(SsaDefinition def, LocalScopeVariable v |
     // alloc via SSA
-    allocReaches(def.getAnUltimateDefiningValue(v), alloc, kind) and
+    allocReaches0(def.getAnUltimateDefiningValue(v), alloc, kind) and
     e = def.getAUse(v)
   ) or exists(Variable v |
-    // alloc via a singly assigned global
+    // alloc via a global
     allocReachesVariable(v, alloc, kind) and
     e.(VariableAccess).getTarget() = v
   )
 }
 
+/**
+ * Holds if `e` is an expression which may evaluate to the
+ * result of previous memory allocations `alloc` only of type
+ * `kind`.
+ */
+predicate allocReaches(Expr e, Expr alloc, string kind) {
+  allocReaches0(e, alloc, kind) and
+  not exists(string k2 |
+    allocReaches0(e, _, k2)  and
+    kind != k2
+  )
+}
+
 /**
  * Holds if `free` is a use of free or delete.  `freed` is the
  * expression that is freed / deleted and `kind` is a string
diff --git a/cpp/ql/test/query-tests/Critical/NewFree/test.cpp b/cpp/ql/test/query-tests/Critical/NewFree/test.cpp
index fd5485ca8766..4fe8559d7eb0 100644
--- a/cpp/ql/test/query-tests/Critical/NewFree/test.cpp
+++ b/cpp/ql/test/query-tests/Critical/NewFree/test.cpp
@@ -337,3 +337,37 @@ class Test11
 
 	char *data;
 };
+
+// ---
+
+int *z;
+
+void test12(bool cond)
+{
+	int *x, *y;
+
+	x = new int();
+	delete x; // GOOD
+	x = (int *)malloc(sizeof(int));
+	free(x); // GOOD
+
+	if (cond)
+	{
+		y = new int();
+		z = new int();
+	} else {
+		y = (int *)malloc(sizeof(int));
+		z = (int *)malloc(sizeof(int));
+	}
+
+	// ...
+
+	if (cond)
+	{
+		delete y; // GOOD
+		delete z; // GOOD
+	} else {
+		free(y); // GOOD
+		free(z); // GOOD
+	}
+}