diff --git a/pybamm/simulation.py b/pybamm/simulation.py
index c8403b1c80..d0797faa98 100644
--- a/pybamm/simulation.py
+++ b/pybamm/simulation.py
@@ -8,6 +8,7 @@
 import warnings
 import sys
 from functools import lru_cache
+from datetime import timedelta
 
 
 def is_notebook():
@@ -718,7 +719,23 @@ def solve(
                     # Use 1-indexing for printing cycle number as it is more
                     # human-intuitive
                     op_conds = self.experiment.operating_conditions[idx]
-                    dt = op_conds["time"]
+
+                    start_time = current_solution.t[-1]
+
+                    # If next step has a timestamp, dt must take that into account
+                    if op_conds["next timestamp"]:
+                        dt = min(
+                            op_conds["time"],
+                            (
+                                op_conds["next timestamp"]
+                                - (
+                                    self.experiment.initial_timestamp
+                                    + timedelta(seconds=float(start_time))
+                                )
+                            ).total_seconds(),
+                        )
+                    else:
+                        dt = op_conds["time"]
                     op_conds_str = op_conds["string"]
                     model = self.op_conds_to_built_models[op_conds_str]
                     solver = self.op_conds_to_built_solvers[op_conds_str]
@@ -727,7 +744,6 @@ def solve(
                     logs["step operating conditions"] = op_conds_str
                     callbacks.on_step_start(logs)
 
-                    start_time = current_solution.t[-1]
                     kwargs["inputs"] = {
                         **user_inputs,
                         **op_conds,
@@ -762,6 +778,8 @@ def solve(
                             # Otherwise, just stop this cycle
                             break
 
+                    # TODO: add rest step if needed!
+
                     steps.append(step_solution)
 
                     cycle_solution = cycle_solution + step_solution
diff --git a/tests/unit/test_experiments/test_simulation_with_experiment.py b/tests/unit/test_experiments/test_simulation_with_experiment.py
index 2d4b201d45..7f19d62d39 100644
--- a/tests/unit/test_experiments/test_simulation_with_experiment.py
+++ b/tests/unit/test_experiments/test_simulation_with_experiment.py
@@ -569,6 +569,29 @@ def test_run_experiment_lead_acid(self):
         sim = pybamm.Simulation(model, experiment=experiment)
         sim.solve()
 
+    def test_run_time_stamped_experiment(self):
+        # experiment = pybamm.Experiment(
+        #     [
+        #         "[2023-01-01 08:00:00] Rest for 1 minute",
+        #         "[2023-01-01 12:00:00] Discharge at 0.5C for 1 hour",
+        #         "[2023-01-01 12:30:00] Charge at 0.1C for 1 hour",
+        #     ]
+        # )
+        experiment = pybamm.Experiment(
+            [
+                "[2023-01-01 08:00:00] Rest for 10 hours",
+                "[2023-01-01 12:00:00] Discharge at 0.5C for 1 hour",
+                "[2023-01-01 12:30:00] Charge at 0.1C for 1 hour",
+            ]
+        )
+        model = pybamm.lithium_ion.SPM()
+        sim = pybamm.Simulation(model, experiment=experiment)
+        sol = sim.solve()
+        sol.plot()
+
+        # TODO: what if a later (beyond next) timestamp should kill current step?
+
+
 
 if __name__ == "__main__":
     print("Add -v for more debug output")