diff --git a/multinet/uploaders/csv.py b/multinet/uploaders/csv.py
index 00fe78c4..3dc50895 100644
--- a/multinet/uploaders/csv.py
+++ b/multinet/uploaders/csv.py
@@ -153,7 +153,12 @@ def upload(
     # Perform validation.
     validate_csv(rows, key, overwrite)
 
-    if key != "_key" and overwrite:
+    # Once we reach here, we know that the specified key field must be present,
+    # and either:
+    #   key == "_key"   # noqa: E800
+    #   or key != "_key" and the "_key" field is not present
+    #   or key != "_key" and "_key" is present, but overwrite = True
+    if key != "_key":
         rows = set_table_key(rows, key)
 
     # Set the collection, paying attention to whether the data contains