diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 72e7373d0dd33..379221478e203 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -130,7 +130,7 @@ Performance Improvements
 
 - Improved performance of :func:`Series.describe` in case of numeric dtpyes (:issue:`21274`)
 - Improved performance of :func:`pandas.core.groupby.GroupBy.rank` when dealing with tied rankings (:issue:`21237`)
-- Improved performance of :func:`DataFrame.set_index` with columns consisting of :class:`Period` objects (:issue:`21582`)
+- Improved performance of :func:`DataFrame.set_index` with columns consisting of :class:`Period` objects (:issue:`21582`,:issue:`21606`)
 -
 
 .. _whatsnew_0240.docs:
diff --git a/pandas/_libs/tslibs/offsets.pyx b/pandas/_libs/tslibs/offsets.pyx
index 63add06db17b4..b4b27b99bdb30 100644
--- a/pandas/_libs/tslibs/offsets.pyx
+++ b/pandas/_libs/tslibs/offsets.pyx
@@ -88,6 +88,15 @@ for _d in DAYS:
 # ---------------------------------------------------------------------
 # Misc Helpers
 
+cdef to_offset(object obj):
+    """
+    Wrap pandas.tseries.frequencies.to_offset to keep centralize runtime
+    imports
+    """
+    from pandas.tseries.frequencies import to_offset
+    return to_offset(obj)
+
+
 def as_datetime(obj):
     f = getattr(obj, 'to_pydatetime', None)
     if f is not None:
@@ -313,6 +322,41 @@ class _BaseOffset(object):
     def __setattr__(self, name, value):
         raise AttributeError("DateOffset objects are immutable.")
 
+    def __eq__(self, other):
+        if is_string_object(other):
+            other = to_offset(other)
+
+        try:
+            return self._params == other._params
+        except AttributeError:
+            # other is not a DateOffset object
+            return False
+
+        return self._params == other._params
+
+    def __ne__(self, other):
+        return not self == other
+
+    def __hash__(self):
+        return hash(self._params)
+
+    @property
+    def _params(self):
+        """
+        Returns a tuple containing all of the attributes needed to evaluate
+        equality between two DateOffset objects.
+        """
+        # NB: non-cython subclasses override property with cache_readonly
+        all_paras = self.__dict__.copy()
+        if 'holidays' in all_paras and not all_paras['holidays']:
+            all_paras.pop('holidays')
+        exclude = ['kwds', 'name', 'calendar']
+        attrs = [(k, v) for k, v in all_paras.items()
+                 if (k not in exclude) and (k[0] != '_')]
+        attrs = sorted(set(attrs))
+        params = tuple([str(self.__class__)] + attrs)
+        return params
+
     @property
     def kwds(self):
         # for backwards-compatibility
diff --git a/pandas/tseries/offsets.py b/pandas/tseries/offsets.py
index a3f82c1a0902e..1cfd3f476f8ab 100644
--- a/pandas/tseries/offsets.py
+++ b/pandas/tseries/offsets.py
@@ -182,6 +182,7 @@ def __add__(date):
 
     Since 0 is a bit weird, we suggest avoiding its use.
     """
+    _params = cache_readonly(BaseOffset._params.fget)
     _use_relativedelta = False
     _adjust_dst = False
     _attributes = frozenset(['n', 'normalize'] +
@@ -288,18 +289,6 @@ def isAnchored(self):
         # if there were a canonical docstring for what isAnchored means.
         return (self.n == 1)
 
-    @cache_readonly
-    def _params(self):
-        all_paras = self.__dict__.copy()
-        if 'holidays' in all_paras and not all_paras['holidays']:
-            all_paras.pop('holidays')
-        exclude = ['kwds', 'name', 'calendar']
-        attrs = [(k, v) for k, v in all_paras.items()
-                 if (k not in exclude) and (k[0] != '_')]
-        attrs = sorted(set(attrs))
-        params = tuple([str(self.__class__)] + attrs)
-        return params
-
     # TODO: Combine this with BusinessMixin version by defining a whitelisted
     # set of attributes on each object rather than the existing behavior of
     # iterating over internal ``__dict__``
@@ -322,24 +311,6 @@ def _repr_attrs(self):
     def name(self):
         return self.rule_code
 
-    def __eq__(self, other):
-
-        if isinstance(other, compat.string_types):
-            from pandas.tseries.frequencies import to_offset
-
-            other = to_offset(other)
-
-        if not isinstance(other, DateOffset):
-            return False
-
-        return self._params == other._params
-
-    def __ne__(self, other):
-        return not self == other
-
-    def __hash__(self):
-        return hash(self._params)
-
     def __add__(self, other):
         if isinstance(other, (ABCDatetimeIndex, ABCSeries)):
             return other + self