diff --git a/lib/core.ts b/lib/core.ts
index d334dc5..dd89163 100644
--- a/lib/core.ts
+++ b/lib/core.ts
@@ -29,6 +29,8 @@ import { visualizeTinyGraph } from "./visualizeTinyGraph"
 export type { StaticallyUnroutableRouteSummary } from "./static-reachability"
 
 const GREEDY_FINAL_ROUTE_MAX_ITERATIONS = 50e3
+export const GREEDY_PANIC_START_FRAC = 0.7
+const DEFAULT_GREEDY_PANIC_START_FRAC = GREEDY_PANIC_START_FRAC
 
 export const createEmptyRegionIntersectionCache =
   (): RegionIntersectionCache => ({
@@ -238,6 +240,7 @@ export interface TinyHyperGraphSolverOptions {
   STATIC_REACHABILITY_PRECHECK_MAX_HOPS?: number
   ACCEPT_BEST_SOLUTION_ON_TIMEOUT?: boolean
   GREEDY_FINAL_ROUTE_ITERS?: number
+  GREEDY_PANIC_START_FRAC?: number
 }
 
 export interface TinyHyperGraphSolverOptionTarget {
@@ -255,6 +258,7 @@ export interface TinyHyperGraphSolverOptionTarget {
   STATIC_REACHABILITY_PRECHECK_MAX_HOPS: number
   ACCEPT_BEST_SOLUTION_ON_TIMEOUT: boolean
   GREEDY_FINAL_ROUTE_ITERS: number
+  GREEDY_PANIC_START_FRAC?: number
 }
 
 export const applyTinyHyperGraphSolverOptions = (
@@ -310,6 +314,9 @@ export const applyTinyHyperGraphSolverOptions = (
   if (options.GREEDY_FINAL_ROUTE_ITERS !== undefined) {
     solver.GREEDY_FINAL_ROUTE_ITERS = options.GREEDY_FINAL_ROUTE_ITERS
   }
+  if (options.GREEDY_PANIC_START_FRAC !== undefined) {
+    solver.GREEDY_PANIC_START_FRAC = options.GREEDY_PANIC_START_FRAC
+  }
 }
 
 export const getTinyHyperGraphSolverOptions = (
@@ -330,6 +337,7 @@ export const getTinyHyperGraphSolverOptions = (
     solver.STATIC_REACHABILITY_PRECHECK_MAX_HOPS,
   ACCEPT_BEST_SOLUTION_ON_TIMEOUT: solver.ACCEPT_BEST_SOLUTION_ON_TIMEOUT,
   GREEDY_FINAL_ROUTE_ITERS: solver.GREEDY_FINAL_ROUTE_ITERS,
+  GREEDY_PANIC_START_FRAC: solver.GREEDY_PANIC_START_FRAC,
 })
 
 const compareCandidatesByF = (left: Candidate, right: Candidate) =>
@@ -375,6 +383,7 @@ export class TinyHyperGraphSolver extends BaseSolver {
   STATIC_REACHABILITY_PRECHECK_MAX_HOPS = 16
   ACCEPT_BEST_SOLUTION_ON_TIMEOUT = true
   GREEDY_FINAL_ROUTE_ITERS = 4
+  GREEDY_PANIC_START_FRAC = DEFAULT_GREEDY_PANIC_START_FRAC
 
   constructor(
     public topology: TinyHyperGraphTopology,
@@ -728,6 +737,35 @@ export class TinyHyperGraphSolver extends BaseSolver {
     )
   }
 
+  protected getGreedyPanicPenaltyScale(): number {
+    if (this.bestSolvedStateSnapshot) {
+      return 1
+    }
+
+    const currentRouteId = this.state.currentRouteId
+    if (
+      currentRouteId === undefined ||
+      this.routeAttemptCountByRouteId[currentRouteId]! <= 1 ||
+      this.routeSuccessCountByRouteId[currentRouteId]! > 0
+    ) {
+      return 1
+    }
+
+    const startFrac = Math.min(1, Math.max(0, this.GREEDY_PANIC_START_FRAC))
+    const maxIterations = Math.max(1, this.MAX_ITERATIONS)
+    const progress = Math.min(1, Math.max(0, this.iterations / maxIterations))
+
+    if (progress <= startFrac) {
+      return 1
+    }
+
+    if (startFrac >= 1) {
+      return 1
+    }
+
+    return Math.max(0, (1 - progress) / (1 - startFrac))
+  }
+
   populateSegmentGeometryScratch(
     regionId: RegionId,
     port1Id: PortId,
@@ -1403,11 +1441,14 @@ export class TinyHyperGraphSolver extends BaseSolver {
         regionCache.existingSegmentCount + 1,
       ) - regionCache.existingRegionCost
 
+    const penaltyScale = this.getGreedyPanicPenaltyScale()
+
     return (
       currentCandidate.g +
       newRegionCost +
-      state.regionCongestionCost[nextRegionId] +
-      (this.problem.portPenalty?.[neighborPortId] ?? 0)
+      (state.regionCongestionCost[nextRegionId] +
+        (this.problem.portPenalty?.[neighborPortId] ?? 0)) *
+        penaltyScale
     )
   }
 
diff --git a/tests/solver/on-all-routes-routed.test.ts b/tests/solver/on-all-routes-routed.test.ts
index 16431f3..59682e1 100644
--- a/tests/solver/on-all-routes-routed.test.ts
+++ b/tests/solver/on-all-routes-routed.test.ts
@@ -1,6 +1,7 @@
 import { expect, test } from "bun:test"
 import {
   type Candidate,
+  GREEDY_PANIC_START_FRAC,
   type TinyHyperGraphProblem,
   TinyHyperGraphSolver,
   type TinyHyperGraphTopology,
@@ -259,6 +260,7 @@ test("constructor options override snake-case hyperparameters before setup", ()
     MAX_ITERATIONS: 1234,
     ACCEPT_BEST_SOLUTION_ON_TIMEOUT: false,
     GREEDY_FINAL_ROUTE_ITERS: 6,
+    GREEDY_PANIC_START_FRAC: 0.8,
   })
 
   expect(solver.DISTANCE_TO_COST).toBe(0.25)
@@ -269,5 +271,38 @@ test("constructor options override snake-case hyperparameters before setup", ()
   expect(solver.MAX_ITERATIONS).toBe(1234)
   expect(solver.ACCEPT_BEST_SOLUTION_ON_TIMEOUT).toBe(false)
   expect(solver.GREEDY_FINAL_ROUTE_ITERS).toBe(6)
+  expect(solver.GREEDY_PANIC_START_FRAC).toBe(0.8)
   expect(solver.problemSetup.portHCostToEndOfRoute[0]).toBe(0.25)
 })
+
+test("soft route penalties linearly drop after the greedy panic start fraction", () => {
+  const solver = createTestSolver({ MAX_ITERATIONS: 100 })
+  const currentCandidate: Candidate = {
+    nextRegionId: 0,
+    portId: 0,
+    f: 2,
+    g: 2,
+    h: 0,
+  }
+
+  solver.state.currentRouteId = 0
+  solver.state.currentRouteNetId = 0
+  solver.state.regionCongestionCost[0] = 6
+  solver.problem.portPenalty = new Float64Array([0, 4, 0, 0])
+  const solverWithProtectedCounters = solver as unknown as {
+    routeAttemptCountByRouteId: Uint32Array
+  }
+  solverWithProtectedCounters.routeAttemptCountByRouteId[0] = 2
+
+  solver.iterations = 0
+  expect(solver.computeG(currentCandidate, 1)).toBe(12)
+
+  solver.iterations = GREEDY_PANIC_START_FRAC * solver.MAX_ITERATIONS
+  expect(solver.computeG(currentCandidate, 1)).toBe(12)
+
+  solver.iterations = 85
+  expect(solver.computeG(currentCandidate, 1)).toBeCloseTo(7)
+
+  solver.iterations = solver.MAX_ITERATIONS
+  expect(solver.computeG(currentCandidate, 1)).toBe(2)
+})