diff --git a/pybamm/simulation.py b/pybamm/simulation.py
index 75d7f14274..6e1be1c6b2 100644
--- a/pybamm/simulation.py
+++ b/pybamm/simulation.py
@@ -471,25 +471,15 @@ def step(
         if solver is None:
             solver = self.solver
 
-        if save is False:
-            # Don't pass previous solution
-            self._solution = solver.step(
-                None,
-                self.built_model,
-                dt,
-                npts=npts,
-                external_variables=external_variables,
-                inputs=inputs,
-            )
-        else:
-            self._solution = solver.step(
-                self._solution,
-                self.built_model,
-                dt,
-                npts=npts,
-                external_variables=external_variables,
-                inputs=inputs,
-            )
+        self._solution = solver.step(
+            self._solution,
+            self.built_model,
+            dt,
+            npts=npts,
+            external_variables=external_variables,
+            inputs=inputs,
+            save=save,
+        )
 
     def get_variable_array(self, *variables):
         """
diff --git a/pybamm/solvers/base_solver.py b/pybamm/solvers/base_solver.py
index 536734fabe..8b9fd509dd 100644
--- a/pybamm/solvers/base_solver.py
+++ b/pybamm/solvers/base_solver.py
@@ -575,7 +575,14 @@ def solve(self, model, t_eval, external_variables=None, inputs=None):
         return solution
 
     def step(
-        self, old_solution, model, dt, npts=2, external_variables=None, inputs=None
+        self,
+        old_solution,
+        model,
+        dt,
+        npts=2,
+        external_variables=None,
+        inputs=None,
+        save=True,
     ):
         """
         Step the solution of the model forward by a given time increment. The
@@ -599,7 +606,8 @@ def step(
             values at the current time
         inputs : dict, optional
             Any input parameters to pass to the model when solving
-
+        save : bool
+            Turn on to store the solution of all previous timesteps
 
         Raises
         ------
@@ -677,7 +685,7 @@ def step(
             pybamm.logger.debug(
                 "Step time: {}".format(timer.format(solution.solve_time))
             )
-        if old_solution is None:
+        if save is False or old_solution is None:
             return solution
         else:
             return old_solution + solution