diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index 97a764fa7dbe8..1a76797afd9b9 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -61,7 +61,7 @@ class ExtensionArray(object):
 
     ExtensionArrays are limited to 1 dimension.
 
-    They may be backed by none, one, or many NumPy ararys. For example,
+    They may be backed by none, one, or many NumPy arrays. For example,
     ``pandas.Categorical`` is an extension array backed by two arrays,
     one for codes and one for categories. An array of IPv6 address may
     be backed by a NumPy structured array with two fields, one for the
@@ -69,6 +69,11 @@ class ExtensionArray(object):
     by some other storage type, like Python lists. Pandas makes no
     assumptions on how the data are stored, just that it can be converted
     to a NumPy array.
+    The ExtensionArray interface does not impose any rules on how this data
+    is stored. However, currently, the backing data cannot be stored in
+    attributes called ``.values`` or ``._values`` to ensure full compatibility
+    with pandas internals. But other names as ``.data``, ``._data``,
+    ``._items``, ... can be freely used.
     """
     # '_typ' is for pandas.core.dtypes.generic.ABCExtensionArray.
     # Don't override this.
diff --git a/pandas/tests/extension/base/interface.py b/pandas/tests/extension/base/interface.py
index 2162552e9650d..9b60652fbace3 100644
--- a/pandas/tests/extension/base/interface.py
+++ b/pandas/tests/extension/base/interface.py
@@ -50,3 +50,9 @@ def test_is_extension_array_dtype(self, data):
         assert is_extension_array_dtype(data.dtype)
         assert is_extension_array_dtype(pd.Series(data))
         assert isinstance(data.dtype, ExtensionDtype)
+
+    def test_no_values_attribute(self, data):
+        # GH-20735: EA's with .values attribute give problems with internal
+        # code, disallowing this for now until solved
+        assert not hasattr(data, 'values')
+        assert not hasattr(data, '_values')
diff --git a/pandas/tests/extension/decimal/array.py b/pandas/tests/extension/decimal/array.py
index a8e88365b5648..bd7d9500fdc14 100644
--- a/pandas/tests/extension/decimal/array.py
+++ b/pandas/tests/extension/decimal/array.py
@@ -30,10 +30,13 @@ class DecimalArray(ExtensionArray):
     def __init__(self, values):
         values = np.asarray(values, dtype=object)
 
-        self.values = values
+        self._data = values
         # Some aliases for common attribute names to ensure pandas supports
         # these
-        self._items = self._data = self.data = self.values
+        self._items = self.data = self._data
+        # those aliases are currently not working due to assumptions
+        # in internal code (GH-20735)
+        # self._values = self.values = self.data
 
     @classmethod
     def _constructor_from_sequence(cls, scalars):
@@ -45,13 +48,13 @@ def _from_factorized(cls, values, original):
 
     def __getitem__(self, item):
         if isinstance(item, numbers.Integral):
-            return self.values[item]
+            return self._data[item]
         else:
-            return type(self)(self.values[item])
+            return type(self)(self._data[item])
 
     def copy(self, deep=False):
         if deep:
-            return type(self)(self.values.copy())
+            return type(self)(self._data.copy())
         return type(self)(self)
 
     def __setitem__(self, key, value):
@@ -59,13 +62,13 @@ def __setitem__(self, key, value):
             value = [decimal.Decimal(v) for v in value]
         else:
             value = decimal.Decimal(value)
-        self.values[key] = value
+        self._data[key] = value
 
     def __len__(self):
-        return len(self.values)
+        return len(self._data)
 
     def __repr__(self):
-        return 'DecimalArray({!r})'.format(self.values)
+        return 'DecimalArray({!r})'.format(self._data)
 
     @property
     def nbytes(self):
@@ -75,7 +78,7 @@ def nbytes(self):
         return 0
 
     def isna(self):
-        return np.array([x.is_nan() for x in self.values])
+        return np.array([x.is_nan() for x in self._data])
 
     def take(self, indexer, allow_fill=True, fill_value=None):
         indexer = np.asarray(indexer)
@@ -86,7 +89,7 @@ def take(self, indexer, allow_fill=True, fill_value=None):
             return type(self)([self._na_value] * len(indexer))
 
         indexer = _ensure_platform_int(indexer)
-        out = self.values.take(indexer)
+        out = self._data.take(indexer)
         out[mask] = self._na_value
 
         return type(self)(out)
@@ -97,7 +100,7 @@ def _na_value(self):
 
     @classmethod
     def _concat_same_type(cls, to_concat):
-        return cls(np.concatenate([x.values for x in to_concat]))
+        return cls(np.concatenate([x._data for x in to_concat]))
 
 
 def make_data():
diff --git a/pandas/tests/extension/json/array.py b/pandas/tests/extension/json/array.py
index 33843492cb706..f5290467203bb 100644
--- a/pandas/tests/extension/json/array.py
+++ b/pandas/tests/extension/json/array.py
@@ -33,6 +33,13 @@ def __init__(self, values):
                 raise TypeError
         self.data = values
 
+        # Some aliases for common attribute names to ensure pandas supports
+        # these
+        self._items = self._data = self.data
+        # those aliases are currently not working due to assumptions
+        # in internal code (GH-20735)
+        # self._values = self.values = self.data
+
     @classmethod
     def _constructor_from_sequence(cls, scalars):
         return cls(scalars)