diff --git a/autolens/analysis/result.py b/autolens/analysis/result.py
index 185aa98ab..b3b8fb21f 100644
--- a/autolens/analysis/result.py
+++ b/autolens/analysis/result.py
@@ -197,6 +197,7 @@ def positions_threshold_from(
         self,
         factor=1.0,
         minimum_threshold=None,
+        maximum_threshold=None,
         positions: Optional[aa.Grid2DIrregular] = None,
         plane_redshift: Optional[float] = None,
     ) -> float:
@@ -224,6 +225,9 @@ def positions_threshold_from(
         minimum_threshold
             The output threshold is rounded up to this value if it is below it, to avoid extremely small threshold
             values.
+        maximum_threshold
+            The output threshold is rounded down to this value if it is above it, to avoid extremely large threshold
+            values.
         positions
             If input, these positions are used instead of the computed multiple image positions from the lens mass
             model.
@@ -257,6 +261,10 @@ def positions_threshold_from(
             if threshold < minimum_threshold:
                 return minimum_threshold
 
+        if maximum_threshold is not None:
+            if threshold > maximum_threshold:
+                return maximum_threshold
+
         return threshold
 
     def positions_likelihood_from(
@@ -380,6 +388,7 @@ def positions_likelihood_from(
         threshold = self.positions_threshold_from(
             factor=factor,
             minimum_threshold=minimum_threshold,
+            maximum_threshold=maximum_threshold,
             positions=positions,
             plane_redshift=plane_redshift,
         )