diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 59cf4c0e2f81d..4548118a61f92 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -4092,8 +4092,11 @@ def drop(
 
         Remove rows or columns by specifying label names and corresponding
         axis, or by specifying directly index or column names. When using a
-        multi-index, labels on different levels can be removed by specifying
-        the level.
+        MultiIndex, labels on different levels can be removed by specifying
+        the level. The now-unused levels remain in the
+        MultiIndex._levels attribute. In case of a MultiIndex either a level
+        must be defined or the labels must be a list of tuples of the same
+        length as the number of levels in the MultiIndex.
 
         Parameters
         ----------
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 8014b16d07b01..0f1be0468aef1 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -4902,7 +4902,9 @@ def isin(self, values, level=None):
 
         Compute boolean array of whether each index value is found in the
         passed set of values. The length of the returned boolean array matches
-        the length of the index.
+        the length of the index. If the index is a multi-index and no level is
+        given, the values must be given as list containing tuples of the same
+        length as the number of levels in the MultiIndex.
 
         Parameters
         ----------