diff --git a/editor/src/plugins/sim/controls.rs b/editor/src/plugins/sim/controls.rs
index 1334f395f0..b20da426c7 100644
--- a/editor/src/plugins/sim/controls.rs
+++ b/editor/src/plugins/sim/controls.rs
@@ -3,7 +3,7 @@ use crate::plugins::{Plugin, PluginCtx};
 use abstutil::elapsed_seconds;
 use ezgui::EventLoopMode;
 use piston::input::Key;
-use sim::{Benchmark, TIMESTEP};
+use sim::{Benchmark, Sim, TIMESTEP};
 use std::mem;
 use std::time::{Duration, Instant};
 
@@ -77,15 +77,51 @@ impl Plugin for SimControls {
                 }
                 if ctx
                     .input
-                    .unimportant_key_pressed(Key::P, SIM, "load sim state")
+                    .unimportant_key_pressed(Key::Y, SIM, "load previous sim state")
                 {
-                    match ctx.primary.sim.load_most_recent() {
+                    match ctx
+                        .primary
+                        .sim
+                        .find_previous_savestate(ctx.primary.sim.time)
+                        .and_then(|path| Sim::load_savestate(path, None))
+                    {
+                        Ok(new_sim) => {
+                            // TODO From the perspective of other SimMode plugins, does this just
+                            // look like the simulation stepping forwards?
+                            ctx.primary.sim = new_sim;
+                            ctx.primary.recalculate_current_selection = true;
+
+                            if let Some((s, _)) = ctx.secondary {
+                                s.sim = Sim::load_savestate(
+                                    s.sim.find_previous_savestate(s.sim.time).unwrap(),
+                                    None,
+                                )
+                                .unwrap();
+                            }
+                        }
+                        Err(e) => error!("Couldn't load savestate: {}", e),
+                    };
+                }
+                if ctx
+                    .input
+                    .unimportant_key_pressed(Key::U, SIM, "load next sim state")
+                {
+                    match ctx
+                        .primary
+                        .sim
+                        .find_next_savestate(ctx.primary.sim.time)
+                        .and_then(|path| Sim::load_savestate(path, None))
+                    {
                         Ok(new_sim) => {
                             ctx.primary.sim = new_sim;
                             ctx.primary.recalculate_current_selection = true;
 
                             if let Some((s, _)) = ctx.secondary {
-                                s.sim = s.sim.load_most_recent().unwrap();
+                                s.sim = Sim::load_savestate(
+                                    s.sim.find_next_savestate(s.sim.time).unwrap(),
+                                    None,
+                                )
+                                .unwrap();
                             }
                         }
                         Err(e) => error!("Couldn't load savestate: {}", e),
diff --git a/sim/src/sim.rs b/sim/src/sim.rs
index 2c25e03c68..c3e1425a7c 100644
--- a/sim/src/sim.rs
+++ b/sim/src/sim.rs
@@ -88,9 +88,15 @@ impl Sim {
         }
     }
 
-    pub fn load(path: String, new_run_name: String) -> Result<Sim, std::io::Error> {
+    pub fn load_savestate(
+        path: String,
+        new_run_name: Option<String>,
+    ) -> Result<Sim, std::io::Error> {
+        info!("Loading {}", path);
         abstutil::read_json(&path).map(|mut s: Sim| {
-            s.run_name = new_run_name;
+            if let Some(name) = new_run_name {
+                s.run_name = name;
+            }
             s
         })
     }
@@ -135,15 +141,8 @@ impl Sim {
             "At {} while processing {:?}",
             self.time, self.current_agent_for_debugging
         );
-        if let Ok(mut list) = self.find_all_savestates() {
-            // Find the most recent one BEFORE the current time
-            list.reverse();
-            for (tick, path) in list {
-                if tick < self.time {
-                    error!("Debug from {}", path);
-                    break;
-                }
-            }
+        if let Ok(path) = self.find_previous_savestate(self.time) {
+            error!("Debug from {}", path);
         }
     }
 
@@ -313,15 +312,6 @@ impl Sim {
         path
     }
 
-    // TODO Return a descriptive error again
-    pub fn load_most_recent(&self) -> Result<Sim, std::io::Error> {
-        let (_, load) = self
-            .find_all_savestates()
-            .and_then(|mut list| list.pop().ok_or_else(|| io_error("empty directory")))?;
-        info!("Loading {}", load);
-        abstutil::read_json(&load)
-    }
-
     // Earliest one is first
     fn find_all_savestates(&self) -> Result<Vec<(Tick, String)>, std::io::Error> {
         let mut results: Vec<(Tick, String)> = Vec::new();
@@ -351,6 +341,28 @@ impl Sim {
         Ok(results)
     }
 
+    pub fn find_previous_savestate(&self, base_time: Tick) -> Result<String, std::io::Error> {
+        let mut list = self.find_all_savestates()?;
+        // Find the most recent one BEFORE the current time
+        list.reverse();
+        for (tick, path) in list {
+            if tick < base_time {
+                return Ok(path);
+            }
+        }
+        Err(io_error(&format!("no savestate before {}", base_time)))
+    }
+
+    pub fn find_next_savestate(&self, base_time: Tick) -> Result<String, std::io::Error> {
+        let list = self.find_all_savestates()?;
+        for (tick, path) in list {
+            if tick > base_time {
+                return Ok(path);
+            }
+        }
+        Err(io_error(&format!("no savestate after {}", base_time)))
+    }
+
     pub fn active_agents(&self) -> Vec<AgentID> {
         self.trips_state.active_agents()
     }
diff --git a/tests/src/sim_determinism.rs b/tests/src/sim_determinism.rs
index 291c5073ee..92a9ac26a1 100644
--- a/tests/src/sim_determinism.rs
+++ b/tests/src/sim_determinism.rs
@@ -89,7 +89,8 @@ pub fn run(t: &mut TestRunner) {
             }
 
             let sim3: sim::Sim =
-                sim::Sim::load(sim1_save.clone(), "with_savestating_3".to_string()).unwrap();
+                sim::Sim::load_savestate(sim1_save.clone(), Some("with_savestating_3".to_string()))
+                    .unwrap();
             if sim3 != sim2 {
                 panic!(
                     "sim state differs between {} and {}",