diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index f5d8a0da0112b..d74673b17c8d9 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -22,14 +22,11 @@ from pandas._libs.tslib import Timestamp, Timedelta
 from datetime import datetime, timedelta, date
 
 from cpython cimport PyTuple_Check, PyList_Check
+from cpython.slice cimport PySlice_Check
 
 cdef int64_t iNaT = util.get_nat()
 
 
-cdef extern from "Python.h":
-    int PySlice_Check(object)
-
-
 cdef inline is_definitely_invalid_key(object val):
     if PyTuple_Check(val):
         try:
diff --git a/pandas/_libs/period.pyx b/pandas/_libs/period.pyx
index 272e6f7d38d87..0a1d4a241b795 100644
--- a/pandas/_libs/period.pyx
+++ b/pandas/_libs/period.pyx
@@ -1,7 +1,6 @@
 # -*- coding: utf-8 -*-
 # cython: profile=False
 from datetime import datetime, date, timedelta
-import operator
 
 from cpython cimport (
     PyUnicode_Check,
@@ -201,7 +200,7 @@ def period_asfreq_arr(ndarray[int64_t] arr, int freq1, int freq2, bint end):
         Py_ssize_t i, n
         freq_conv_func func
         asfreq_info finfo
-        int64_t val, ordinal
+        int64_t val
         char relation
 
     n = len(arr)
@@ -236,9 +235,6 @@ def period_asfreq_arr(ndarray[int64_t] arr, int freq1, int freq2, bint end):
 
 def period_ordinal(int y, int m, int d, int h, int min,
                    int s, int us, int ps, int freq):
-    cdef:
-        int64_t ordinal
-
     return get_period_ordinal(y, m, d, h, min, s, us, ps, freq)
 
 
diff --git a/pandas/_libs/tslib.pyx b/pandas/_libs/tslib.pyx
index a32f04fe7b156..0777b83de4645 100644
--- a/pandas/_libs/tslib.pyx
+++ b/pandas/_libs/tslib.pyx
@@ -5,7 +5,7 @@
 # distutils: define_macros=CYTHON_TRACE_NOGIL=0
 
 cimport numpy as np
-from numpy cimport (int8_t, int32_t, int64_t, import_array, ndarray,
+from numpy cimport (int32_t, int64_t, import_array, ndarray,
                     float64_t, NPY_DATETIME, NPY_TIMEDELTA)
 import numpy as np
 
@@ -24,8 +24,6 @@ from cpython cimport (
 cdef extern from "Python.h":
     cdef PyTypeObject *Py_TYPE(object)
 
-from libc.stdlib cimport free
-
 from util cimport (is_integer_object, is_float_object, is_string_object,
                    is_datetime64_object, is_timedelta64_object,
                    INT64_MAX)
@@ -51,7 +49,6 @@ from tslibs.np_datetime cimport (check_dts_bounds,
                                  PANDAS_DATETIMEUNIT, PANDAS_FR_ns,
                                  dt64_to_dtstruct, dtstruct_to_dt64,
                                  pydatetime_to_dt64, pydate_to_dt64,
-                                 npy_datetime,
                                  get_datetime64_unit, get_datetime64_value,
                                  get_timedelta64_value,
                                  days_per_month_table,
@@ -75,12 +72,10 @@ from tslibs.timedeltas cimport cast_from_unit, delta_to_nanoseconds
 from tslibs.timedeltas import Timedelta
 from tslibs.timezones cimport (
     is_utc, is_tzlocal, is_fixed_offset,
-    treat_tz_as_dateutil, treat_tz_as_pytz,
-    get_timezone, get_utcoffset, maybe_get_tz,
+    treat_tz_as_pytz,
+    get_timezone, maybe_get_tz,
     get_dst_info)
-from tslibs.fields import (
-    get_date_name_field, get_start_end_field, get_date_field,
-    build_field_sarray)
+from tslibs.fields import get_start_end_field, get_date_field
 from tslibs.conversion cimport (tz_convert_single, _TSObject,
                                 convert_to_tsobject,
                                 convert_datetime_to_tsobject,
@@ -1763,13 +1758,6 @@ cpdef array_to_datetime(ndarray[object] values, errors='raise',
         return oresult
 
 
-cdef PyTypeObject* td_type = <PyTypeObject*> Timedelta
-
-
-cdef inline bint is_timedelta(object o):
-    return Py_TYPE(o) == td_type  # isinstance(o, Timedelta)
-
-
 # ----------------------------------------------------------------------
 # Conversion routines
 
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index b0e22460fdcb0..ba96979435f81 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -55,7 +55,7 @@
 from pandas._libs import (lib, index as libindex, tslib as libts,
                           algos as libalgos, join as libjoin,
                           Timestamp, period as libperiod)
-from pandas._libs.tslibs import timezones, conversion
+from pandas._libs.tslibs import timezones, conversion, fields
 
 # -------- some conversion wrapper functions
 
@@ -75,20 +75,20 @@ def f(self):
                                                self.freq.kwds.get('month', 12))
                             if self.freq else 12)
 
-                result = libts.get_start_end_field(values, field, self.freqstr,
-                                                   month_kw)
+                result = fields.get_start_end_field(values, field,
+                                                    self.freqstr, month_kw)
             else:
-                result = libts.get_date_field(values, field)
+                result = fields.get_date_field(values, field)
 
             # these return a boolean by-definition
             return result
 
         if field in self._object_ops:
-            result = libts.get_date_name_field(values, field)
+            result = fields.get_date_name_field(values, field)
             result = self._maybe_mask_results(result)
 
         else:
-            result = libts.get_date_field(values, field)
+            result = fields.get_date_field(values, field)
             result = self._maybe_mask_results(result, convert='float64')
 
         return Index(result, name=self.name)