diff --git a/sqlite_utils/db.py b/sqlite_utils/db.py
index e819d17..1f85338 100644
--- a/sqlite_utils/db.py
+++ b/sqlite_utils/db.py
@@ -2660,8 +2660,6 @@ class Table(Queryable):
 
             def convert_value(v):
                 bar.update(1)
-                if not v:
-                    return v
                 return jsonify_if_needed(fn(v))
 
             self.db.register_function(convert_value)
diff --git a/sqlite_utils/recipes.py b/sqlite_utils/recipes.py
index ac41954..cf31ee8 100644
--- a/sqlite_utils/recipes.py
+++ b/sqlite_utils/recipes.py
@@ -14,6 +14,8 @@ def parsedate(value, dayfirst=False, yearfirst=False, errors=None):
     - errors=r.IGNORE to ignore values that cannot be parsed
     - errors=r.SET_NULL to set values that cannot be parsed to null
     """
+    if not value:
+        return value
     try:
         return (
             parser.parse(value, dayfirst=dayfirst, yearfirst=yearfirst)
@@ -38,6 +40,8 @@ def parsedatetime(value, dayfirst=False, yearfirst=False, errors=None):
     - errors=r.IGNORE to ignore values that cannot be parsed
     - errors=r.SET_NULL to set values that cannot be parsed to null
     """
+    if not value:
+        return value
     try:
         return parser.parse(value, dayfirst=dayfirst, yearfirst=yearfirst).isoformat()
     except parser.ParserError:
@@ -53,4 +57,6 @@ def jsonsplit(value, delimiter=",", type=str):
     """
     Convert a string like a,b,c into a JSON array ["a", "b", "c"]
     """
+    if not value:
+        return value
     return json.dumps([type(s.strip()) for s in value.split(delimiter)])
diff --git a/tests/test_cli_convert.py b/tests/test_cli_convert.py
index d26ab8c..49627df 100644
--- a/tests/test_cli_convert.py
+++ b/tests/test_cli_convert.py
@@ -80,7 +80,8 @@ def test_convert_import(test_db_and_path):
             db_path,
             "example",
             "dt",
-            "return re.sub('O..', 'OXX', value)",
+            #"return re.sub('O..', 'OXX', value)",
+            "return None if value is None else re.sub('O..', 'OXX', value)",
             "--import",
             "re",
         ],
@@ -223,7 +224,7 @@ def test_convert_output_column(test_db_and_path, drop):
         db_path,
         "example",
         "dt",
-        "value.replace('October', 'Spooktober')",
+        "None if value is None else value.replace('October', 'Spooktober')",
         "--output",
         "newcol",
     ]