diff --git a/cf/test/test_Field.py b/cf/test/test_Field.py
index 881ddbb3eb..92a72ff8a8 100644
--- a/cf/test/test_Field.py
+++ b/cf/test/test_Field.py
@@ -1,6 +1,7 @@
 import atexit
 import datetime
 import faulthandler
+from importlib.util import find_spec
 import itertools
 import os
 import re
@@ -1152,6 +1153,8 @@ def test_Field_insert_dimension(self):
         with self.assertRaises(ValueError):
             f.insert_dimension(1, "qwerty")
 
+    @unittest.skipUnless(
+        find_spec("matplotlib"), "matplotlib required but not installed")
     def test_Field_indices(self):
         f = cf.read(self.filename)[0]
 
diff --git a/cf/test/test_RegridOperator.py b/cf/test/test_RegridOperator.py
index dae6be8ce8..d92bf9b554 100644
--- a/cf/test/test_RegridOperator.py
+++ b/cf/test/test_RegridOperator.py
@@ -1,5 +1,6 @@
 import datetime
 import faulthandler
+from importlib.util import find_spec
 import unittest
 
 faulthandler.enable()  # to debug seg faults and timeouts
@@ -7,11 +8,23 @@
 import cf
 
 
+# ESMF renamed its Python module to `esmpy` at ESMF version 8.4.0. Allow
+# either for now for backwards compatibility.
+esmpy_imported = False
+# Note: here only need esmpy for cf under-the-hood code, not in test
+# directly, so no need to actually import esmpy, just test it is there.
+if find_spec("esmpy") or find_spec("ESMF"):
+    esmpy_imported = True
+
+
 class RegridOperatorTest(unittest.TestCase):
-    src = cf.example_field(0)
-    dst = cf.example_field(1)
-    r = src.regrids(dst, "linear", return_operator=True)
 
+    def setUp(self):
+        src = cf.example_field(0)
+        dst = cf.example_field(1)
+        self.r = src.regrids(dst, "linear", return_operator=True)
+
+    @unittest.skipUnless(esmpy_imported, "Requires esmpy/ESMF package.")
     def test_RegridOperator_attributes(self):
         self.assertEqual(self.r.coord_sys, "spherical")
         self.assertEqual(self.r.method, "linear")
@@ -39,6 +52,7 @@ def test_RegridOperator_attributes(self):
         self.assertIsNone(self.r.dst_z)
         self.assertFalse(self.r.ln_z)
 
+    @unittest.skipUnless(esmpy_imported, "Requires esmpy/ESMF package.")
     def test_RegridOperator_copy(self):
         self.assertIsInstance(self.r.copy(), self.r.__class__)
 
diff --git a/cf/test/test_read_write.py b/cf/test/test_read_write.py
index 82e3e919e8..2810c335ed 100644
--- a/cf/test/test_read_write.py
+++ b/cf/test/test_read_write.py
@@ -4,6 +4,7 @@
 import inspect
 import os
 import shutil
+import shutil
 import subprocess
 import tempfile
 import unittest
@@ -642,6 +643,8 @@ def test_read_write_unlimited(self):
         self.assertTrue(domain_axes["domainaxis0"].nc_is_unlimited())
         self.assertTrue(domain_axes["domainaxis2"].nc_is_unlimited())
 
+    @unittest.skipUnless(
+        shutil.which("ncdump"), "ncdump required - install nco")
     def test_read_CDL(self):
         subprocess.run(
             " ".join(["ncdump", self.filename, ">", tmpfile]),
@@ -703,6 +706,8 @@ def test_read_CDL(self):
         with self.assertRaises(Exception):
             cf.read("test_read_write.py")
 
+    @unittest.skipUnless(
+        shutil.which("ncdump"), "ncdump required - install nco")
     def test_read_cdl_string(self):
         """Test the cf.read 'cdl_string' keyword."""
         f = cf.read("example_field_0.nc")[0]
@@ -876,6 +881,8 @@ def test_read_url(self):
             f = cf.read(remote)
             self.assertEqual(len(f), 1)
 
+    @unittest.skipUnless(
+        shutil.which("ncdump"), "ncdump required - install nco")
     def test_read_dataset_type(self):
         """Test the cf.read 'dataset_type' keyword."""
         # netCDF dataset
diff --git a/cf/test/test_regrid_featureType.py b/cf/test/test_regrid_featureType.py
index 198b44dd97..3a1967f3d5 100644
--- a/cf/test/test_regrid_featureType.py
+++ b/cf/test/test_regrid_featureType.py
@@ -36,11 +36,6 @@
 atol = 2e-12
 rtol = 0
 
-meshloc = {
-    "face": esmpy.MeshLoc.ELEMENT,
-    "node": esmpy.MeshLoc.NODE,
-}
-
 
 def esmpy_regrid(coord_sys, method, src, dst, **kwargs):
     """Helper function that regrids one dimension of Field data using
@@ -53,6 +48,11 @@ def esmpy_regrid(coord_sys, method, src, dst, **kwargs):
         Regridded numpy masked array.
 
     """
+    meshloc = {
+        "face": esmpy.MeshLoc.ELEMENT,
+        "node": esmpy.MeshLoc.NODE,
+    }
+
     esmpy_regrid = cf.regrid.regrid(
         coord_sys,
         src,
diff --git a/cf/test/test_regrid_mesh.py b/cf/test/test_regrid_mesh.py
index 3095640135..39e29f26fe 100644
--- a/cf/test/test_regrid_mesh.py
+++ b/cf/test/test_regrid_mesh.py
@@ -39,11 +39,6 @@
 atol = 2e-12
 rtol = 0
 
-meshloc = {
-    "face": esmpy.MeshLoc.ELEMENT,
-    "node": esmpy.MeshLoc.NODE,
-}
-
 
 def esmpy_regrid(coord_sys, method, src, dst, **kwargs):
     """Helper function that regrids one dimension of Field data using
@@ -56,6 +51,11 @@ def esmpy_regrid(coord_sys, method, src, dst, **kwargs):
         Regridded numpy masked array.
 
     """
+    meshloc = {
+        "face": esmpy.MeshLoc.ELEMENT,
+        "node": esmpy.MeshLoc.NODE,
+    }
+
     esmpy_regrid = cf.regrid.regrid(
         coord_sys,
         src,
diff --git a/cf/test/test_style.py b/cf/test/test_style.py
index 13ab4b45ec..907cfd892b 100644
--- a/cf/test/test_style.py
+++ b/cf/test/test_style.py
@@ -1,10 +1,9 @@
 import datetime
 import faulthandler
+from importlib.util import find_spec
 import os
 import unittest
 
-import pycodestyle
-
 faulthandler.enable()  # to debug seg faults and timeouts
 
 import cf
@@ -31,7 +30,11 @@ def setUp(self):
             for path in non_cf_python_files
         ]
 
+    @unittest.skipUnless(
+        find_spec("pycodestyle"), "pycodestyle required but not installed")
     def test_pep8_compliance(self):
+        import pycodestyle
+
         pep8_check = pycodestyle.StyleGuide()
 
         # Directories to skip in the recursive walk of the directory: