diff --git a/docs/design/sim.md b/docs/design/sim.md
index 4f57c246a4..6a145ba7db 100644
--- a/docs/design/sim.md
+++ b/docs/design/sim.md
@@ -136,7 +136,7 @@ though... Can we fork RNG for that too?
 Problems:
 - CarIDs are different, could make them be original parking spot
 - Missing trip ID, different ped IDs
-- gen_range on different inputs
+= gen_range on different inputs
 
 
 
diff --git a/sim/src/lib.rs b/sim/src/lib.rs
index b6fdf8ea42..514e0eea61 100644
--- a/sim/src/lib.rs
+++ b/sim/src/lib.rs
@@ -59,6 +59,7 @@ use geom::{Angle, Pt2D};
 pub use helpers::{load, SimFlags};
 pub use instrument::save_backtraces;
 use map_model::{LaneID, Trace, TurnID};
+use rand::{Rng, SeedableRng, XorShiftRng};
 pub use scenario::{Neighborhood, Scenario, SeedParkedCars, SpawnOverTime};
 pub use sim::{Benchmark, Sim};
 use std::fmt;
@@ -322,3 +323,7 @@ impl Cloneable for Scenario {}
 impl Cloneable for Tick {}
 impl Cloneable for MapEdits {}
 impl Cloneable for ABTest {}
+
+fn fork_rng<R: Rng + ?Sized>(base_rng: &mut R) -> XorShiftRng {
+    XorShiftRng::from_seed([base_rng.next_u32() as u8; 16])
+}
diff --git a/sim/src/scenario.rs b/sim/src/scenario.rs
index 145d4bcc06..8c02067cc6 100644
--- a/sim/src/scenario.rs
+++ b/sim/src/scenario.rs
@@ -2,8 +2,8 @@ use abstutil;
 use geom::{Polygon, Pt2D};
 use map_model::{BuildingID, LaneID, Map};
 use rand::Rng;
-use std::collections::HashMap;
-use {ParkedCar, Sim, Tick};
+use std::collections::{BTreeMap, HashMap};
+use {fork_rng, ParkedCar, Sim, Tick};
 
 #[derive(Clone, Serialize, Deserialize, Debug)]
 pub struct Scenario {
@@ -101,7 +101,7 @@ impl Scenario {
             );
         }
 
-        let mut parked_cars_per_neighborhood: HashMap<String, Vec<ParkedCar>> = HashMap::new();
+        let mut parked_cars_per_neighborhood: BTreeMap<String, Vec<ParkedCar>> = BTreeMap::new();
         for (name, neighborhood) in &neighborhoods {
             parked_cars_per_neighborhood.insert(
                 name.to_string(),
@@ -109,6 +109,11 @@ impl Scenario {
                     .get_all_parked_cars(Some(&Polygon::new(&neighborhood.points))),
             );
         }
+        // Shuffle the list of parked cars, but be sure to fork the RNG to be stable across map
+        // edits.
+        for cars in parked_cars_per_neighborhood.values_mut() {
+            fork_rng(&mut sim.rng).shuffle(cars);
+        }
 
         for s in &self.spawn_over_time {
             for _ in 0..s.num_agents {
@@ -126,22 +131,16 @@ impl Scenario {
                     .unwrap();
 
                 if sim.rng.gen_bool(s.percent_drive) {
-                    if parked_cars_per_neighborhood[&s.start_from_neighborhood].is_empty() {
-                        panic!(
-                            "{} has no parked cars; can't instantiate {}",
-                            s.start_from_neighborhood, self.scenario_name
-                        );
-                    }
                     // TODO Probably prefer parked cars close to from_bldg, unless the particular
                     // area is tight on parking. :)
-                    let idx = sim.rng.gen_range(
-                        0,
-                        parked_cars_per_neighborhood[&s.start_from_neighborhood].len(),
-                    );
                     let parked_car = parked_cars_per_neighborhood
                         .get_mut(&s.start_from_neighborhood)
                         .unwrap()
-                        .remove(idx);
+                        .pop()
+                        .expect(&format!(
+                            "{} has no parked cars; can't instantiate {}",
+                            s.start_from_neighborhood, self.scenario_name
+                        ));
 
                     sim.spawner.start_trip_using_parked_car(
                         spawn_time,
diff --git a/sim/src/spawn.rs b/sim/src/spawn.rs
index a64267fed2..609aed36b1 100644
--- a/sim/src/spawn.rs
+++ b/sim/src/spawn.rs
@@ -3,14 +3,16 @@ use driving::DrivingSimState;
 use kinematics::Vehicle;
 use map_model::{BuildingID, BusRoute, BusStopID, LaneID, Map, Pathfinder};
 use parking::ParkingSimState;
-use rand::{Rng, SeedableRng, XorShiftRng};
+use rand::Rng;
 use router::Router;
 use std::collections::VecDeque;
 use std::time::Instant;
 use transit::TransitSimState;
 use trips::{TripLeg, TripManager};
 use walking::{SidewalkSpot, WalkingSimState};
-use {AgentID, CarID, Event, ParkedCar, ParkingSpot, PedestrianID, RouteID, Tick, TripID};
+use {
+    fork_rng, AgentID, CarID, Event, ParkedCar, ParkingSpot, PedestrianID, RouteID, Tick, TripID,
+};
 
 #[derive(Serialize, Deserialize, PartialEq, Eq, Debug)]
 enum Command {
@@ -213,7 +215,7 @@ impl Spawner {
         // Fork a new RNG for each candidate lane. This keeps things more deterministic, invariant
         // of lane edits.
         for l in in_lanes.into_iter() {
-            let mut rng = XorShiftRng::from_seed([base_rng.next_u32() as u8; 16]);
+            let mut rng = fork_rng(base_rng);
 
             for spot in parking_sim.get_free_spots(l) {
                 total_capacity += 1;