diff --git a/neurolib/optimize/exploration/exploration.py b/neurolib/optimize/exploration/exploration.py
index 717577f4..c39db0b4 100644
--- a/neurolib/optimize/exploration/exploration.py
+++ b/neurolib/optimize/exploration/exploration.py
@@ -281,6 +281,8 @@ def getModelFromTraj(self, traj):
         """
         model = self.model
         runParams = self.getParametersFromTraj(traj)
+        if self.parameterSpace.star:
+            runParams = flatten_nested_dict(flat_dict_to_nested(runParams)["parameters"])
 
         model.params.update(runParams)
         return model
diff --git a/neurolib/utils/stimulus.py b/neurolib/utils/stimulus.py
index 60febf7f..8e72e57e 100644
--- a/neurolib/utils/stimulus.py
+++ b/neurolib/utils/stimulus.py
@@ -80,9 +80,20 @@ def update_params(self, params_dict):
         :param params_dict: New parameters for this input
         :type params_dict: dict
         """
+
+        def _sanitize(value):
+            """
+            Change string `None` to actual None - can happen with Exploration or
+            Evolution, since `pypet` does None -> "None".
+            """
+            if value == "None":
+                return None
+            else:
+                return value
+
         for param, value in params_dict.items():
             if hasattr(self, param):
-                setattr(self, param, value)
+                setattr(self, param, _sanitize(value))
 
     def _get_times(self, duration, dt):
         """
diff --git a/tests/test_exploration.py b/tests/test_exploration.py
index 68bc8464..b20c648a 100644
--- a/tests/test_exploration.py
+++ b/tests/test_exploration.py
@@ -20,7 +20,7 @@
 
 
 def randomString(stringLength=10):
-    """Generate a random string of fixed length """
+    """Generate a random string of fixed length"""
     letters = string.ascii_lowercase
     return "".join(random.choice(letters) for i in range(stringLength))
 
diff --git a/tests/test_stimulus.py b/tests/test_stimulus.py
index 7ccbec76..82ad5ca1 100644
--- a/tests/test_stimulus.py
+++ b/tests/test_stimulus.py
@@ -238,7 +238,7 @@ def test_set_params(self):
             n=2,
             seed=42,
         )
-        UPDATE = {"amplitude": 43.0, "seed": 12}
+        UPDATE = {"amplitude": 43.0, "seed": 12, "start": "None"}
         sin.update_params(UPDATE)
         params = sin.get_params()
         params.pop("type")
@@ -249,10 +249,10 @@ def test_set_params(self):
                 "seed": 42,
                 "frequency": self.FREQUENCY,
                 "amplitude": self.AMPLITUDE,
-                "start": STIM_START,
                 "dc_bias": False,
                 "end": STIM_END,
                 **UPDATE,
+                "start": None,
             },
         )
 
@@ -318,7 +318,7 @@ def test_set_params(self):
             n=2,
             seed=42,
         )
-        UPDATE = {"amplitude": 43.0, "seed": 12}
+        UPDATE = {"amplitude": 43.0, "seed": 12, "start": "None"}
         sq.update_params(UPDATE)
         params = sq.get_params()
         params.pop("type")
@@ -329,10 +329,10 @@ def test_set_params(self):
                 "seed": 42,
                 "frequency": self.FREQUENCY,
                 "amplitude": self.AMPLITUDE,
-                "start": STIM_START,
                 "end": STIM_END,
                 "dc_bias": False,
                 **UPDATE,
+                "start": None,
             },
         )