diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index 24f3e4433411e..0fc862210fc6e 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -301,6 +301,7 @@ Indexing
 - Bug in :func:`MultiIndex.remove_unused_levels` which would fill nan values (:issue:`18417`)
 - Bug in :func:`MultiIndex.from_tuples`` which would fail to take zipped tuples in python3 (:issue:`18434`)
 - Bug in :class:`Index` construction from list of mixed type tuples (:issue:`18505`)
+- Bug in :func:`Index.drop` when passing a list of both tuples and non-tuples (:issue:`18304`)
 - Bug in :class:`IntervalIndex` where empty and purely NA data was constructed inconsistently depending on the construction method (:issue:`18421`)
 - Bug in :func:`IntervalIndex.symmetric_difference` where the symmetric difference with a non-``IntervalIndex`` did not raise (:issue:`18475`)
 - Bug in indexing a datetimelike ``Index`` that raised ``ValueError`` instead of ``IndexError`` (:issue:`18386`).
diff --git a/pandas/core/common.py b/pandas/core/common.py
index 35696be5b2a03..775ecc32b0f3c 100644
--- a/pandas/core/common.py
+++ b/pandas/core/common.py
@@ -398,7 +398,19 @@ def _asarray_tuplesafe(values, dtype=None):
     return result
 
 
-def _index_labels_to_array(labels):
+def _index_labels_to_array(labels, dtype=None):
+    """
+    Transform label or iterable of labels to array, for use in Index.
+
+    Parameters
+    ----------
+    dtype : dtype
+        If specified, use as dtype of the resulting array, otherwise infer.
+
+    Returns
+    -------
+    array
+    """
     if isinstance(labels, (compat.string_types, tuple)):
         labels = [labels]
 
@@ -408,7 +420,7 @@ def _index_labels_to_array(labels):
         except TypeError:  # non-iterable
             labels = [labels]
 
-    labels = _asarray_tuplesafe(labels)
+    labels = _asarray_tuplesafe(labels, dtype=dtype)
 
     return labels
 
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 78c7cb7b1d30c..04b8ade7e5253 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -3761,7 +3761,8 @@ def drop(self, labels, errors='raise'):
         -------
         dropped : Index
         """
-        labels = _index_labels_to_array(labels)
+        arr_dtype = 'object' if self.dtype == 'object' else None
+        labels = _index_labels_to_array(labels, dtype=arr_dtype)
         indexer = self.get_indexer(labels)
         mask = indexer == -1
         if mask.any():
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index e09f4ad360843..e33fd1e0f4c1e 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -1429,6 +1429,27 @@ def test_drop(self):
         expected = Index([1, 2])
         tm.assert_index_equal(dropped, expected)
 
+    @pytest.mark.parametrize("values", [['a', 'b', ('c', 'd')],
+                                        ['a', ('c', 'd'), 'b'],
+                                        [('c', 'd'), 'a', 'b']])
+    @pytest.mark.parametrize("to_drop", [[('c', 'd'), 'a'], ['a', ('c', 'd')]])
+    def test_drop_tuple(self, values, to_drop):
+        # GH 18304
+        index = pd.Index(values)
+        expected = pd.Index(['b'])
+
+        result = index.drop(to_drop)
+        tm.assert_index_equal(result, expected)
+
+        removed = index.drop(to_drop[0])
+        for drop_me in to_drop[1], [to_drop[1]]:
+            result = removed.drop(drop_me)
+            tm.assert_index_equal(result, expected)
+
+        removed = index.drop(to_drop[1])
+        for drop_me in to_drop[1], [to_drop[1]]:
+            pytest.raises(ValueError, removed.drop, drop_me)
+
     def test_tuple_union_bug(self):
         import pandas
         import numpy as np
diff --git a/pandas/tests/reshape/test_pivot.py b/pandas/tests/reshape/test_pivot.py
index 6b44a339fad73..5b64f62527da4 100644
--- a/pandas/tests/reshape/test_pivot.py
+++ b/pandas/tests/reshape/test_pivot.py
@@ -1631,3 +1631,15 @@ def test_crosstab_dup_index_names(self):
                                 index=expected_index,
                                 columns=expected_index)
         tm.assert_frame_equal(result, expected)
+
+    @pytest.mark.parametrize("names", [['a', ('b', 'c')],
+                                       [('a', 'b'), 'c']])
+    def test_crosstab_tuple_name(self, names):
+        s1 = pd.Series(range(3), name=names[0])
+        s2 = pd.Series(range(1, 4), name=names[1])
+
+        mi = pd.MultiIndex.from_arrays([range(3), range(1, 4)], names=names)
+        expected = pd.Series(1, index=mi).unstack(1, fill_value=0)
+
+        result = pd.crosstab(s1, s2)
+        tm.assert_frame_equal(result, expected)