diff --git a/src/components/Inspector.vue b/src/components/Inspector.vue
index b439625..7ad6650 100644
--- a/src/components/Inspector.vue
+++ b/src/components/Inspector.vue
@@ -115,6 +115,8 @@ const RULE_HINT: Record<Rule["kind"], string> = {
   constant: "A fixed number — no inputs.",
   proportional: "rate = factor × its “+” inputs.",
   gap: "rate = factor × (level − target): the “+” input is the level, the “−” the target.",
+  overflow:
+    "rate = max(0, factor × (level − threshold)): spills only once the “+” level passes the “−” threshold.",
 }
 </script>
 
@@ -167,6 +169,7 @@ const RULE_HINT: Record<Rule["kind"], string> = {
             <option value="constant">Constant</option>
             <option value="proportional">Proportional</option>
             <option value="gap">Gap</option>
+            <option value="overflow">Overflow</option>
           </select>
         </label>
 
diff --git a/src/model/io.ts b/src/model/io.ts
index fada8c8..8778db8 100644
--- a/src/model/io.ts
+++ b/src/model/io.ts
@@ -55,7 +55,8 @@ function isPolarity(value: unknown): value is Polarity {
 function isRule(value: unknown): value is Rule {
   if (!isObject(value)) return false
   if (value.kind === "constant") return isFiniteNumber(value.value)
-  if (value.kind === "proportional" || value.kind === "gap") return isFiniteNumber(value.factor)
+  if (value.kind === "proportional" || value.kind === "gap" || value.kind === "overflow")
+    return isFiniteNumber(value.factor)
   return false
 }
 
diff --git a/src/model/simulation.ts b/src/model/simulation.ts
index e54948b..5d3660f 100644
--- a/src/model/simulation.ts
+++ b/src/model/simulation.ts
@@ -107,6 +107,19 @@ function evalRule(rule: Rule, links: InformationLink[], valueOf: (id: string) =>
         rule.factor * ((level ? valueOf(level.source) : 0) - (target ? valueOf(target.source) : 0))
       )
     }
+    case "overflow": {
+      // max(0, factor × (level − threshold)): a one-sided gap. The `+` input is the
+      // level, the `−` the threshold; it stays shut until the level passes it, so an
+      // overflow Flow spills only the excess. Clamping at 0 is what stops it running
+      // backwards below the threshold — gap can't, by design (it's bidirectional).
+      const level = links.find((link) => link.polarity === "+")
+      const threshold = links.find((link) => link.polarity === "-")
+      return Math.max(
+        0,
+        rule.factor *
+          ((level ? valueOf(level.source) : 0) - (threshold ? valueOf(threshold.source) : 0)),
+      )
+    }
   }
 }
 
diff --git a/src/model/types.ts b/src/model/types.ts
index 00af745..23981aa 100644
--- a/src/model/types.ts
+++ b/src/model/types.ts
@@ -42,11 +42,15 @@ export interface Position {
  *                     (→ exponential growth/decay)
  *  - `gap`          — `factor × (level − target)`, where the `+` input is the
  *                     level and the `−` input the target. (→ goal-seeking)
+ *  - `overflow`     — `max(0, factor × (level − threshold))`: a one-sided `gap`
+ *                     that only fires once the `+` level exceeds the `−`
+ *                     threshold. (→ a spillway / hard ceiling)
  */
 export type Rule =
   | { kind: "constant"; value: number }
   | { kind: "proportional"; factor: number }
   | { kind: "gap"; factor: number }
+  | { kind: "overflow"; factor: number }
 
 /**
  * The run parameters for a simulation: integrate from `start` to `stop` in steps