diff --git a/pandas/core/indexes/api.py b/pandas/core/indexes/api.py
index e50a4b099a8e1..b3a3f758e05b1 100644
--- a/pandas/core/indexes/api.py
+++ b/pandas/core/indexes/api.py
@@ -54,95 +54,111 @@ def _get_objs_combined_axis(objs, intersect=False, axis=0, sort=True):
 
 
 def _get_combined_index(indexes, intersect=False, sort=False):
-    # TODO: handle index names!
-    indexes = com.get_distinct_objs(indexes)
-    if len(indexes) == 0:
-        index = Index([])
-    elif len(indexes) == 1:
-        index = indexes[0]
-    elif intersect:
-        index = indexes[0]
-        for other in indexes[1:]:
-            index = index.intersection(other)
+    if intersect:
+        return _intersect_indexes(indexes, sort=sort)
     else:
-        index = _union_indexes(indexes, sort=sort)
-        index = ensure_index(index)
+        return _union_indexes(indexes, sort=sort)
+
+
+def _intersect_indexes(indexes, sort=True):
+    """Return the intersection of indexes
+    """
+    if len(indexes) == 0:
+        return Index([])  # TODO
+
+    indexes = com.get_distinct_objs(indexes)  # distinct ids
 
+    result = indexes[0]
+    for other in indexes[1:]:
+        result = result.intersection(other)
+        
     if sort:
-        try:
-            index = index.sort_values()
-        except TypeError:
-            pass
-    return index
+        result = _maybe_sort(result)
+
+    # TODO: names
+
+    return result
 
 
 def _union_indexes(indexes, sort=True):
     if len(indexes) == 0:
-        raise AssertionError('Must have at least 1 Index to union')
-    if len(indexes) == 1:
-        result = indexes[0]
-        if isinstance(result, list):
-            result = Index(sorted(result))
-        return result
+        return Index([])
+
+    indexes = com.get_distinct_objs(indexes)
 
+    # convert lists to indexes
+    # check if at least one 'special'
     indexes, kind = _sanitize_and_check(indexes)
 
-    def _unique_indices(inds):
-        def conv(i):
-            if isinstance(i, Index):
-                i = i.tolist()
-            return i
+    if kind == 'special':
+        return _union_indexes_special(indexes, sort=sort)
+    else:
+        return _union_indexes_no_special(indexes, sort=sort)
 
-        return Index(
-            lib.fast_unique_multiple_list([conv(i) for i in inds], sort=sort))
 
-    if kind == 'special':
+def _union_indexes_special(indexes, sort=True):
+    if sort:
         result = indexes[0]
 
-        if hasattr(result, 'union_many'):
+        if hasattr(result, 'union_many'):  # DatetimeIndex
             return result.union_many(indexes[1:])
         else:
             for other in indexes[1:]:
                 result = result.union(other)
             return result
-    elif kind == 'array':
-        index = indexes[0]
-        for other in indexes[1:]:
-            if not index.equals(other):
-
-                if sort is None:
-                    # TODO: remove once pd.concat sort default changes
-                    warnings.warn(_sort_msg, FutureWarning, stacklevel=8)
-                    sort = True
+    else:
+        raise NotImplementedError
 
-                return _unique_indices(indexes)
 
+def _union_indexes_no_special(indexes, sort=True):
+    index = indexes[0]
+    if _all_indexes_same(indexes):
+        # name handled here
         name = _get_consensus_names(indexes)[0]
         if name != index.name:
             index = index._shallow_copy(name=name)
+        if sort:
+            index = _maybe_sort(index)
         return index
-    else:  # kind='list'
-        return _unique_indices(indexes)
+    else:
+        # but not here
+        if sort is None:
+            # TODO: remove once pd.concat and df.append sort default changes
+            warnings.warn(_sort_msg, FutureWarning, stacklevel=8)
+            sort = True
+        return _unique_indices(indexes, sort=sort)
 
 
 def _sanitize_and_check(indexes):
-    kinds = list({type(index) for index in indexes})
+    kinds = {type(index) for index in indexes}
 
     if list in kinds:
         if len(kinds) > 1:
-            indexes = [Index(com.try_sort(x))
-                       if not isinstance(x, Index) else
-                       x for x in indexes]
+            # e.g. indexes = [Index([2, 3]), [[1, 2]])
+            indexes = [Index(x) if isinstance(x, list) else x
+                       for x in indexes]
             kinds.remove(list)
         else:
+            #e.g. indexes = [[1, 2]]
             return indexes, 'list'
 
     if len(kinds) > 1 or Index not in kinds:
+        # equivalent to any(kind != Index for kind in kinds)
         return indexes, 'special'
     else:
         return indexes, 'array'
 
 
+def _unique_indices(inds, sort=sort):
+    def conv(i):
+        if isinstance(i, Index):
+            i = i.tolist()
+        return i
+
+    return Index(
+        lib.fast_unique_multiple_list([conv(i) for i in inds], sort=sort))
+
+
 def _get_consensus_names(indexes):
 
     # find the non-none names, need to tupleify to make