diff --git a/src/passes/ConstraintAnalysis.cpp b/src/passes/ConstraintAnalysis.cpp
index fff4e4b8ed3..89a3584487c 100644
--- a/src/passes/ConstraintAnalysis.cpp
+++ b/src/passes/ConstraintAnalysis.cpp
@@ -568,14 +568,6 @@ struct ConstraintAnalysis
         return;
       }
 
-      // See above on binary action counting limits.
-      if (auto* binary = set->value->dynCast<Binary>()) {
-        if (binaryActionCounts[binary]++ >= MaxBinaryActions) {
-          constraints.setProvesNothing(set->index);
-          return;
-        }
-      }
-
       // Look at the fallthrough. It is valid to do so, because our constraints
       // only track two things, constants and locals. For a constant, it does
       // not change while falling through. For a local, the only way for the
@@ -600,8 +592,37 @@ struct ConstraintAnalysis
       // opportunity to write any other value while falling through. (And, any
       // local.tee appearing here would have been reached earlier in the
       // traversal, and handled.)
-      auto* value =
-        Properties::getFallthrough(set->value, getPassOptions(), *getModule());
+      auto* value = set->value;
+      while (1) {
+        if (value->is<LocalSet>()) {
+          // We stop at the first tee: we don't need to look any further, and
+          // will just apply that local's values to ourselves, saving repeated
+          // work.
+          break;
+        }
+        auto* next = Properties::getImmediateFallthrough(
+          value, getPassOptions(), *getModule());
+        if (value == next) {
+          break;
+        } else {
+          value = next;
+        }
+      }
+
+      // Now that we know the value, check binary action counting limits (see
+      // above).
+      if (auto* binary = value->dynCast<Binary>()) {
+        // The count may exceed the limit sometimes, but add a hard assert on
+        // never going up so high it is likely doing an unbounded computation.
+        auto& count = binaryActionCounts[binary];
+        assert(count < MaxBinaryActions * 10);
+        count++;
+        if (count >= MaxBinaryActions) {
+          constraints.setProvesNothing(set->index);
+          return;
+        }
+      }
+
       constraints.set(set->index, value);
     }
   }
diff --git a/test/lit/passes/constraint-analysis-loops.wast b/test/lit/passes/constraint-analysis-loops.wast
index 9c1e594f18e..7c66ee84429 100644
--- a/test/lit/passes/constraint-analysis-loops.wast
+++ b/test/lit/passes/constraint-analysis-loops.wast
@@ -1905,4 +1905,59 @@
       )
     )
   )
+
+  ;; CHECK:      (func $increment-tee (type $0)
+  ;; CHECK-NEXT:  (local $x i32)
+  ;; CHECK-NEXT:  (local $y i32)
+  ;; CHECK-NEXT:  (loop $label1
+  ;; CHECK-NEXT:   (if
+  ;; CHECK-NEXT:    (i32.gt_s
+  ;; CHECK-NEXT:     (local.get $y)
+  ;; CHECK-NEXT:     (local.get $x)
+  ;; CHECK-NEXT:    )
+  ;; CHECK-NEXT:    (then
+  ;; CHECK-NEXT:     (unreachable)
+  ;; CHECK-NEXT:    )
+  ;; CHECK-NEXT:   )
+  ;; CHECK-NEXT:   (local.set $y
+  ;; CHECK-NEXT:    (local.tee $x
+  ;; CHECK-NEXT:     (i32.add
+  ;; CHECK-NEXT:      (local.get $y)
+  ;; CHECK-NEXT:      (i32.const 1)
+  ;; CHECK-NEXT:     )
+  ;; CHECK-NEXT:    )
+  ;; CHECK-NEXT:   )
+  ;; CHECK-NEXT:   (br $label1)
+  ;; CHECK-NEXT:  )
+  ;; CHECK-NEXT: )
+  (func $increment-tee
+    (local $x i32)
+    (local $y i32)
+    ;; A loop, where $y is incremented but there is a tee in the middle. The loop
+    ;; is unbounded (the exit condition is never hit), so we must be careful to
+    ;; not keep calculating 1,2,3, without limit. The tee in the middle should not
+    ;; confuse us: we apply the +=1 operation to x directly, but y reads it
+    ;; through the tee. We should stop calculating anything about both rather than
+    ;; hang for a long time.
+    (loop $label1
+      (if
+        (i32.gt_s
+          (local.get $y)
+          (local.get $x)
+        )
+        (then
+          (unreachable)
+        )
+      )
+      (local.set $y
+        (local.tee $x
+          (i32.add
+            (local.get $y)
+            (i32.const 1)
+          )
+        )
+      )
+      (br $label1)
+    )
+  )
 )