diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 8cb384f50d371..efd4028f2eada 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -513,7 +513,7 @@ Missing
 MultiIndex
 ^^^^^^^^^^
 
--
+- Removed compatibility for MultiIndex pickles prior to version 0.8.0; compatibility with MultiIndex pickles from version 0.13 forward is maintained (:issue:`21654`)
 -
 -
 
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 7d24a901382bb..4912014b43773 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -824,15 +824,6 @@ def values(self):
         self._tuples = lib.fast_zip(values)
         return self._tuples
 
-    # fml
-    @property
-    def _is_v1(self):
-        return False
-
-    @property
-    def _is_v2(self):
-        return False
-
     @property
     def _has_complex_internals(self):
         # to disable groupby tricks
@@ -2843,22 +2834,6 @@ def delete(self, loc):
         return MultiIndex(levels=self.levels, labels=new_labels,
                           names=self.names, verify_integrity=False)
 
-    get_major_bounds = slice_locs
-
-    __bounds = None
-
-    @property
-    def _bounds(self):
-        """
-        Return or compute and return slice points for level 0, assuming
-        sortedness
-        """
-        if self.__bounds is None:
-            inds = np.arange(len(self.levels[0]))
-            self.__bounds = self.labels[0].searchsorted(inds)
-
-        return self.__bounds
-
     def _wrap_joined_index(self, joined, other):
         names = self.names if self.names == other.names else None
         return MultiIndex.from_tuples(joined, names=names)
diff --git a/pandas/tests/indexes/multi/data/mindex_073.pickle b/pandas/tests/indexes/multi/data/mindex_073.pickle
deleted file mode 100644
index c99f51fa289ac..0000000000000
Binary files a/pandas/tests/indexes/multi/data/mindex_073.pickle and /dev/null differ
diff --git a/pandas/tests/indexes/multi/data/multiindex_v1.pickle b/pandas/tests/indexes/multi/data/multiindex_v1.pickle
deleted file mode 100644
index d404a78f9e397..0000000000000
--- a/pandas/tests/indexes/multi/data/multiindex_v1.pickle
+++ /dev/null
@@ -1,149 +0,0 @@
-cnumpy.core.multiarray
-_reconstruct
-p0
-(cpandas.core.index
-MultiIndex
-p1
-(I0
-tp2
-S'b'
-p3
-tp4
-Rp5
-((I1
-(I10
-tp6
-cnumpy
-dtype
-p7
-(S'O8'
-p8
-I0
-I1
-tp9
-Rp10
-(I3
-S'|'
-p11
-NNNI-1
-I-1
-I63
-tp12
-bI00
-(lp13
-I0
-aI1
-aI2
-aI3
-aI4
-aI5
-aI6
-aI7
-aI8
-aI9
-atp14
-((lp15
-g0
-(cpandas.core.index
-Index
-p16
-(I0
-tp17
-g3
-tp18
-Rp19
-((I1
-(I4
-tp20
-g10
-I00
-(lp21
-S'foo'
-p22
-aS'bar'
-p23
-aS'baz'
-p24
-aS'qux'
-p25
-atp26
-(S'first'
-p27
-tp28
-tp29
-bag0
-(g16
-(I0
-tp30
-g3
-tp31
-Rp32
-((I1
-(I3
-tp33
-g10
-I00
-(lp34
-S'one'
-p35
-aS'two'
-p36
-aS'three'
-p37
-atp38
-(S'second'
-p39
-tp40
-tp41
-ba(lp42
-g0
-(cnumpy
-ndarray
-p43
-(I0
-tp44
-g3
-tp45
-Rp46
-(I1
-(I10
-tp47
-g7
-(S'i4'
-p48
-I0
-I1
-tp49
-Rp50
-(I3
-S'<'
-p51
-NNNI-1
-I-1
-I0
-tp52
-bI00
-S'\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x01\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x02\x00\x00\x00\x03\x00\x00\x00\x03\x00\x00\x00\x03\x00\x00\x00'
-p53
-tp54
-bag0
-(g43
-(I0
-tp55
-g3
-tp56
-Rp57
-(I1
-(I10
-tp58
-g50
-I00
-S'\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x01\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00\x00\x00\x00\x00\x01\x00\x00\x00\x02\x00\x00\x00'
-p59
-tp60
-baN(lp61
-g27
-ag39
-atp62
-tp63
-b.
\ No newline at end of file
diff --git a/pandas/tests/indexes/multi/test_analytics.py b/pandas/tests/indexes/multi/test_analytics.py
index 4cc0504417801..9f6a72f803f9d 100644
--- a/pandas/tests/indexes/multi/test_analytics.py
+++ b/pandas/tests/indexes/multi/test_analytics.py
@@ -15,10 +15,6 @@ def test_shift(idx):
     pytest.raises(NotImplementedError, idx.shift, 1, 2)
 
 
-def test_bounds(idx):
-    idx._bounds
-
-
 def test_groupby(idx):
     groups = idx.groupby(np.array([1, 1, 1, 2, 2, 2]))
     labels = idx.get_values().tolist()
diff --git a/pandas/tests/indexes/multi/test_conversion.py b/pandas/tests/indexes/multi/test_conversion.py
index ab99679af0f1a..fcc22390e17a1 100644
--- a/pandas/tests/indexes/multi/test_conversion.py
+++ b/pandas/tests/indexes/multi/test_conversion.py
@@ -4,10 +4,8 @@
 import numpy as np
 import pandas as pd
 import pandas.util.testing as tm
-import pytest
 from pandas import DataFrame, MultiIndex, date_range
-from pandas.compat import PY3, range
-from pandas.util.testing import assert_almost_equal
+from pandas.compat import range
 
 
 def test_tolist(idx):
@@ -93,46 +91,6 @@ def test_to_hierarchical():
     assert result.names == index.names
 
 
-@pytest.mark.skipif(PY3, reason="testing legacy pickles not support on py3")
-def test_legacy_pickle(datapath):
-
-    path = datapath('indexes', 'multi', 'data', 'multiindex_v1.pickle')
-    obj = pd.read_pickle(path)
-
-    obj2 = MultiIndex.from_tuples(obj.values)
-    assert obj.equals(obj2)
-
-    res = obj.get_indexer(obj)
-    exp = np.arange(len(obj), dtype=np.intp)
-    assert_almost_equal(res, exp)
-
-    res = obj.get_indexer(obj2[::-1])
-    exp = obj.get_indexer(obj[::-1])
-    exp2 = obj2.get_indexer(obj2[::-1])
-    assert_almost_equal(res, exp)
-    assert_almost_equal(exp, exp2)
-
-
-def test_legacy_v2_unpickle(datapath):
-
-    # 0.7.3 -> 0.8.0 format manage
-    path = datapath('indexes', 'multi', 'data', 'mindex_073.pickle')
-    obj = pd.read_pickle(path)
-
-    obj2 = MultiIndex.from_tuples(obj.values)
-    assert obj.equals(obj2)
-
-    res = obj.get_indexer(obj)
-    exp = np.arange(len(obj), dtype=np.intp)
-    assert_almost_equal(res, exp)
-
-    res = obj.get_indexer(obj2[::-1])
-    exp = obj.get_indexer(obj[::-1])
-    exp2 = obj2.get_indexer(obj2[::-1])
-    assert_almost_equal(res, exp)
-    assert_almost_equal(exp, exp2)
-
-
 def test_roundtrip_pickle_with_tz():
 
     # GH 8367
@@ -146,6 +104,7 @@ def test_roundtrip_pickle_with_tz():
 
 
 def test_pickle(indices):
+
     unpickled = tm.round_trip_pickle(indices)
     assert indices.equals(unpickled)
     original_name, indices.name = indices.name, 'foo'