diff --git a/sqlite_utils/db.py b/sqlite_utils/db.py
index e97f71d..36dec86 100644
--- a/sqlite_utils/db.py
+++ b/sqlite_utils/db.py
@@ -456,31 +456,24 @@ class Table:
 
     @property
     def pks(self):
-        return [column.name for column in self.columns if column.is_pk]
+        names = [column.name for column in self.columns if column.is_pk]
+        if not names:
+            names = ["rowid"]
+        return names
 
     def get(self, pk_values):
         if not isinstance(pk_values, (list, tuple)):
             pk_values = [pk_values]
         pks = self.pks
-        pk_names = []
-        if len(pks) == 0:
-            # rowid table
-            pk_names = ["rowid"]
-            last_pk = pk_values[0]
-        elif len(pks) == 1:
-            pk_names = [pks[0]]
-            last_pk = pk_values[0]
-        elif len(pks) > 1:
-            pk_names = pks
-            last_pk = pk_values
-        if len(pk_names) != len(pk_values):
+        last_pk = pk_values[0] if len(pks) == 1 else pk_values
+        if len(pks) != len(pk_values):
             raise NotFoundError(
                 "Need {} primary key value{}".format(
-                    len(pk_names), "" if len(pk_names) == 1 else "s"
+                    len(pks), "" if len(pks) == 1 else "s"
                 )
             )
 
-        wheres = ["[{}] = ?".format(pk_name) for pk_name in pk_names]
+        wheres = ["[{}] = ?".format(pk_name) for pk_name in pks]
         rows = self.rows_where(" and ".join(wheres), pk_values)
         try:
             row = list(rows)[0]
@@ -788,26 +781,15 @@ class Table:
         updates = updates or {}
         if not isinstance(pk_values, (list, tuple)):
             pk_values = [pk_values]
-        pks = self.pks
-        pk_names = []
-        if len(pks) == 0:
-            # rowid table
-            pk_names = ["rowid"]
-            last_pk = pk_values[0]
-        elif len(pks) == 1:
-            pk_names = [pks[0]]
-            last_pk = pk_values[0]
-        elif len(pks) > 1:
-            pk_names = pks
-            last_pk = pk_values
-        assert len(pk_names) == len(pk_values)
+        # Sanity check that the record exists (raises error if not):
+        self.get(pk_values)
         args = []
         sets = []
         wheres = []
         for key, value in updates.items():
             sets.append("[{}] = ?".format(key))
             args.append(value)
-        wheres = ["[{}] = ?".format(pk_name) for pk_name in pk_names]
+        wheres = ["[{}] = ?".format(pk_name) for pk_name in self.pks]
         args.extend(pk_values)
         sql = "update [{table}] set {sets} where {wheres}".format(
             table=self.name, sets=", ".join(sets), wheres=" and ".join(wheres)
@@ -816,7 +798,7 @@ class Table:
             rowcount = self.db.conn.execute(sql, args).rowcount
             # TODO: Test this works (rolls back) - use better exception:
             assert rowcount == 1
-        self.last_pk = last_pk
+        self.last_pk = pk_values[0] if len(self.pks) == 1 else pk_values
         return self
 
     def insert(
diff --git a/tests/test_introspect.py b/tests/test_introspect.py
index 0dd544e..d3ab27a 100644
--- a/tests/test_introspect.py
+++ b/tests/test_introspect.py
@@ -98,3 +98,11 @@ def test_guess_foreign_table(fresh_db, column, expected_table_guess):
     fresh_db.create_table("authors", {"name": str})
     fresh_db.create_table("genre", {"name": str})
     assert expected_table_guess == fresh_db["books"].guess_foreign_table(column)
+
+
+@pytest.mark.parametrize(
+    "pk,expected", ((None, ["rowid"]), ("id", ["id"]), (["id", "id2"], ["id", "id2"]))
+)
+def test_pks(fresh_db, pk, expected):
+    fresh_db["foo"].insert_all([{"id": 1, "id2": 2}], pk=pk)
+    assert expected == fresh_db["foo"].pks