diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 3bf6dce00a031..868f0553816d0 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -35,7 +35,7 @@
 from pandas.core.indexes.base import Index, _index_shared_docs
 from pandas.core.tools.timedeltas import to_timedelta
 
-from pandas.tseries.frequencies import to_offset
+from pandas.tseries.frequencies import DateOffset, to_offset
 
 _index_doc_kwargs = dict(ibase._index_doc_kwargs)
 
@@ -71,6 +71,36 @@ def method(self, other):
     return method
 
 
+class DatetimeTimedeltaMixin:
+    """
+    Mixin class for methods shared by DatetimeIndex and TimedeltaIndex,
+    but not PeriodIndex
+    """
+
+    def _set_freq(self, freq):
+        """
+        Set the _freq attribute on our underlying DatetimeArray.
+
+        Parameters
+        ----------
+        freq : DateOffset, None, or "infer"
+        """
+        # GH#29843
+        if freq is None:
+            # Always valid
+            pass
+        elif len(self) == 0 and isinstance(freq, DateOffset):
+            # Always valid.  In the TimedeltaIndex case, we assume this
+            #  is a Tick offset.
+            pass
+        else:
+            # As an internal method, we can ensure this assertion always holds
+            assert freq == "infer"
+            freq = to_offset(self.inferred_freq)
+
+        self._data._freq = freq
+
+
 class DatetimeIndexOpsMixin(ExtensionOpsMixin):
     """
     Common ops mixin to support a unified interface datetimelike Index.
@@ -592,8 +622,7 @@ def intersection(self, other, sort=False):
             result = Index.intersection(self, other, sort=sort)
             if isinstance(result, type(self)):
                 if result.freq is None:
-                    # TODO: find a less code-smelly way to set this
-                    result._data._freq = to_offset(result.inferred_freq)
+                    result._set_freq("infer")
             return result
 
         elif (
@@ -608,8 +637,7 @@ def intersection(self, other, sort=False):
             # Invalidate the freq of `result`, which may not be correct at
             # this point, depending on the values.
 
-            # TODO: find a less code-smelly way to set this
-            result._data._freq = None
+            result._set_freq(None)
             if hasattr(self, "tz"):
                 result = self._shallow_copy(
                     result._values, name=result.name, tz=result.tz, freq=None
@@ -617,8 +645,7 @@ def intersection(self, other, sort=False):
             else:
                 result = self._shallow_copy(result._values, name=result.name, freq=None)
             if result.freq is None:
-                # TODO: find a less code-smelly way to set this
-                result._data._freq = to_offset(result.inferred_freq)
+                result._set_freq("infer")
             return result
 
         # to make our life easier, "sort" the two ranges
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 1fd962dd24656..c81d1076f1015 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -34,6 +34,7 @@
 from pandas.core.indexes.datetimelike import (
     DatetimeIndexOpsMixin,
     DatetimelikeDelegateMixin,
+    DatetimeTimedeltaMixin,
     ea_passthrough,
 )
 from pandas.core.indexes.numeric import Int64Index
@@ -93,7 +94,9 @@ class DatetimeDelegateMixin(DatetimelikeDelegateMixin):
     typ="method",
     overwrite=False,
 )
-class DatetimeIndex(DatetimeIndexOpsMixin, Int64Index, DatetimeDelegateMixin):
+class DatetimeIndex(
+    DatetimeTimedeltaMixin, DatetimeIndexOpsMixin, Int64Index, DatetimeDelegateMixin
+):
     """
     Immutable ndarray of datetime64 data, represented internally as int64, and
     which can be boxed to Timestamp objects that are subclasses of datetime and
@@ -412,7 +415,7 @@ def _convert_for_op(self, value):
     @Appender(Index.difference.__doc__)
     def difference(self, other, sort=None):
         new_idx = super().difference(other, sort=sort)
-        new_idx._data._freq = None
+        new_idx._set_freq(None)
         return new_idx
 
     # --------------------------------------------------------------------
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 889075ebe4e31..23a42b7173c2c 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -29,6 +29,7 @@
 from pandas.core.indexes.datetimelike import (
     DatetimeIndexOpsMixin,
     DatetimelikeDelegateMixin,
+    DatetimeTimedeltaMixin,
     ea_passthrough,
 )
 from pandas.core.indexes.numeric import Int64Index
@@ -64,7 +65,11 @@ class TimedeltaDelegateMixin(DatetimelikeDelegateMixin):
     overwrite=True,
 )
 class TimedeltaIndex(
-    DatetimeIndexOpsMixin, dtl.TimelikeOps, Int64Index, TimedeltaDelegateMixin
+    DatetimeTimedeltaMixin,
+    DatetimeIndexOpsMixin,
+    dtl.TimelikeOps,
+    Int64Index,
+    TimedeltaDelegateMixin,
 ):
     """
     Immutable ndarray of timedelta64 data, represented internally as int64, and
@@ -296,8 +301,7 @@ def _union(self, other, sort):
             result = Index._union(this, other, sort=sort)
             if isinstance(result, TimedeltaIndex):
                 if result.freq is None:
-                    # TODO: find a less code-smelly way to set this
-                    result._data._freq = to_offset(result.inferred_freq)
+                    result._set_freq("infer")
             return result
 
     def join(self, other, how="left", level=None, return_indexers=False, sort=False):
@@ -350,8 +354,7 @@ def intersection(self, other, sort=False):
     @Appender(Index.difference.__doc__)
     def difference(self, other, sort=None):
         new_idx = super().difference(other, sort=sort)
-        # TODO: find a less code-smelly way to set this
-        new_idx._data._freq = None
+        new_idx._set_freq(None)
         return new_idx
 
     def _wrap_joined_index(self, joined, other):
diff --git a/pandas/core/resample.py b/pandas/core/resample.py
index 2294c846e81c7..bcac5c4d2913b 100644
--- a/pandas/core/resample.py
+++ b/pandas/core/resample.py
@@ -1025,8 +1025,7 @@ def _downsample(self, how, **kwargs):
         if not len(ax):
             # reset to the new freq
             obj = obj.copy()
-            # TODO: find a less code-smelly way to set this
-            obj.index._data._freq = self.freq
+            obj.index._set_freq(self.freq)
             return obj
 
         # do we have a regular frequency