diff --git a/asv_bench/benchmarks/categoricals.py b/asv_bench/benchmarks/categoricals.py
index 6f43a6fd3fc9b..107b9b9edcd5d 100644
--- a/asv_bench/benchmarks/categoricals.py
+++ b/asv_bench/benchmarks/categoricals.py
@@ -258,9 +258,6 @@ def setup(self):
     def time_get_loc(self):
         self.index.get_loc(self.category)
 
-    def time_shape(self):
-        self.index.shape
-
     def time_shallow_copy(self):
         self.index._shallow_copy()
 
diff --git a/asv_bench/benchmarks/index_cached_properties.py b/asv_bench/benchmarks/index_cached_properties.py
index 13b33855569c9..16fbc741775e4 100644
--- a/asv_bench/benchmarks/index_cached_properties.py
+++ b/asv_bench/benchmarks/index_cached_properties.py
@@ -7,6 +7,7 @@ class IndexCache:
 
     params = [
         [
+            "CategoricalIndex",
             "DatetimeIndex",
             "Float64Index",
             "IntervalIndex",
@@ -42,6 +43,8 @@ def setup(self, index_type):
             self.idx = pd.Float64Index(range(N))
         elif index_type == "UInt64Index":
             self.idx = pd.UInt64Index(range(N))
+        elif index_type == "CategoricalIndex":
+            self.idx = pd.CategoricalIndex(range(N), range(N))
         else:
             raise ValueError
         assert len(self.idx) == N
diff --git a/asv_bench/benchmarks/index_object.py b/asv_bench/benchmarks/index_object.py
index cf51a4d35f805..b242de6a17208 100644
--- a/asv_bench/benchmarks/index_object.py
+++ b/asv_bench/benchmarks/index_object.py
@@ -55,14 +55,6 @@ def time_datetime_difference_disjoint(self):
         self.datetime_left.difference(self.datetime_right)
 
 
-class Datetime:
-    def setup(self):
-        self.dr = date_range("20000101", freq="D", periods=10000)
-
-    def time_is_dates_only(self):
-        self.dr._is_dates_only
-
-
 class Range:
     def setup(self):
         self.idx_inc = RangeIndex(start=0, stop=10 ** 7, step=3)
diff --git a/asv_bench/benchmarks/indexing.py b/asv_bench/benchmarks/indexing.py
index 087fe3916845b..e98d2948e76ea 100644
--- a/asv_bench/benchmarks/indexing.py
+++ b/asv_bench/benchmarks/indexing.py
@@ -1,3 +1,8 @@
+"""
+These benchmarks are for Series and DataFrame indexing methods.  For the
+lower-level methods directly on Index and subclasses, see index_object.py,
+indexing_engine.py, and index_cached.py
+"""
 import warnings
 
 import numpy as np
diff --git a/asv_bench/benchmarks/period.py b/asv_bench/benchmarks/period.py
index b52aa2e55af35..e15d4c66e4fc0 100644
--- a/asv_bench/benchmarks/period.py
+++ b/asv_bench/benchmarks/period.py
@@ -85,9 +85,6 @@ def setup(self):
     def time_get_loc(self):
         self.index.get_loc(self.period)
 
-    def time_shape(self):
-        self.index.shape
-
     def time_shallow_copy(self):
         self.index._shallow_copy()
 
diff --git a/asv_bench/benchmarks/timedelta.py b/asv_bench/benchmarks/timedelta.py
index 208c8f9d14a5e..cfe05c3e257b1 100644
--- a/asv_bench/benchmarks/timedelta.py
+++ b/asv_bench/benchmarks/timedelta.py
@@ -73,9 +73,6 @@ def setup(self):
     def time_get_loc(self):
         self.index.get_loc(self.timedelta)
 
-    def time_shape(self):
-        self.index.shape
-
     def time_shallow_copy(self):
         self.index._shallow_copy()
 
diff --git a/asv_bench/benchmarks/timeseries.py b/asv_bench/benchmarks/timeseries.py
index e3ed33456ee44..6c9f8ee77e5ad 100644
--- a/asv_bench/benchmarks/timeseries.py
+++ b/asv_bench/benchmarks/timeseries.py
@@ -57,6 +57,9 @@ def time_to_date(self, index_type):
     def time_to_pydatetime(self, index_type):
         self.index.to_pydatetime()
 
+    def time_is_dates_only(self, index_type):
+        self.index._is_dates_only
+
 
 class TzLocalize: