diff --git a/pyproject.toml b/pyproject.toml
index b614c65eba..11f809acf8 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "splink"
-version = "0.4.1"
+version = "0.4.2"
 description = "Implementation in Apache Spark of the EM algorithm to estimate parameters of Fellegi-Sunter's canonical model of record linkage."
 authors = ["Robin Linacre <robinlinacre@hotmail.com>", "Sam Lindsay", "Theodore Manassis"]
 license = "MIT"
diff --git a/splink/estimate.py b/splink/estimate.py
index 566e0acef6..7282d26983 100644
--- a/splink/estimate.py
+++ b/splink/estimate.py
@@ -105,6 +105,8 @@ def estimate_u_values(
 
     for i, col in enumerate(orig_settings["comparison_columns"]):
         u_probs = new_settings["comparison_columns"][i]["u_probabilities"]
+        # Ensure non-zero u (https://github.com/moj-analytical-services/splink/issues/161)
+        u_probs = [u or 1/target_rows for u in u_probs]
         col["u_probabilities"] = u_probs
 
     return orig_settings
diff --git a/splink/settings.py b/splink/settings.py
index f9a909cf39..8c4828d07f 100644
--- a/splink/settings.py
+++ b/splink/settings.py
@@ -162,6 +162,19 @@ def _complete_probabilities(col_settings: dict, setting_name: str):
         levels = col_settings["num_levels"]
         probs = col_settings[setting_name]
 
+        # Check for m and u manually set to zero (https://github.com/moj-analytical-services/splink/issues/161)
+        if not all(col_settings[setting_name]):
+            if "custom_name" in col_settings:
+                col_name = col_settings["custom_name"]
+            else:
+                col_name = col_settings["col_name"]
+            warnings.warn(
+                f"Your {setting_name} for {col_name} include zeroes."
+                f"Where {letter}=0 for a given level, it remains fixed rather than being estimated"
+                "along with other model parameters, and all comparisons at this level"
+                f"are assigned a match score of {1. if letter=='u' else 0.}, regardless of other comparisons columns."
+                )
+
         if len(probs) != levels:
             raise ValueError(
                 f"Number of {setting_name} provided is not equal to number of levels specified"