diff --git a/.appveyor.yml b/.appveyor.yml
index 9ec837996d1..553ccdff128 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -80,7 +80,7 @@ test_script:
 - cd c:\pillow
 - '%PYTHON%\%PIP_DIR%\pip.exe install pytest pytest-cov'
 - c:\"Program Files (x86)"\"Windows Kits"\10\Debuggers\x86\gflags.exe /p /enable %PYTHON%\%EXECUTABLE%
-- '%PYTHON%\%EXECUTABLE% -m pytest -vx --cov PIL --cov-report term --cov-report xml Tests'
+- '%PYTHON%\%EXECUTABLE% -m pytest -vx --cov PIL --cov Tests --cov-report term --cov-report xml Tests'
 #- '%PYTHON%\%EXECUTABLE% test-installed.py -v -s %TEST_OPTIONS%' TODO TEST_OPTIONS with pytest?
 
 after_test:
diff --git a/.codecov.yml b/.codecov.yml
index a93095486ce..d348345dc70 100644
--- a/.codecov.yml
+++ b/.codecov.yml
@@ -9,3 +9,10 @@ codecov:
   token: 6dafc396-e7f5-4221-a38a-8b07a49fbdae
 
 comment: off
+
+# Matches 'omit:' in .coveragerc
+ignore:
+  - "Tests/32bit_segfault_check.py"
+  - "Tests/bench_cffi_access.py"
+  - "Tests/check_*.py"
+  - "Tests/createfontdatachunk.py"
diff --git a/.coveragerc b/.coveragerc
index ea79190ae0e..f1f095806e5 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -12,3 +12,10 @@ exclude_lines =
     # Don't complain about debug code
     if Image.DEBUG:
     if DEBUG:
+
+[run]
+omit =
+    Tests/32bit_segfault_check.py
+    Tests/bench_cffi_access.py
+    Tests/check_*.py
+    Tests/createfontdatachunk.py
diff --git a/.github/workflows/test-windows.yml b/.github/workflows/test-windows.yml
index 5877b128025..00cae9bc2c7 100644
--- a/.github/workflows/test-windows.yml
+++ b/.github/workflows/test-windows.yml
@@ -351,7 +351,7 @@ jobs:
         rem Add libraqm.dll (copied to INCLIB) to PATH.
         path %INCLIB%;%PATH%
         cd /D %GITHUB_WORKSPACE%
-        %PYTHON%\python.exe -m pytest -vx --cov PIL --cov-report term --cov-report xml Tests
+        %PYTHON%\python.exe -m pytest -vx --cov PIL --cov Tests --cov-report term --cov-report xml Tests
       shell: cmd
 
     - name: Upload errors
diff --git a/.travis/test.sh b/.travis/test.sh
index a65e620b88a..91dae9f8d37 100755
--- a/.travis/test.sh
+++ b/.travis/test.sh
@@ -2,7 +2,7 @@
 
 set -e
 
-python -m pytest -v -x --cov PIL --cov-report term Tests
+python -m pytest -v -x --cov PIL --cov Tests --cov-report term Tests
 
 # Docs
 if [ "$TRAVIS_PYTHON_VERSION" == "3.7" ]; then make doccheck; fi
diff --git a/Tests/README.rst b/Tests/README.rst
index da3297bcea7..9c959a4bf9d 100644
--- a/Tests/README.rst
+++ b/Tests/README.rst
@@ -27,6 +27,6 @@ Run all the tests from the root of the Pillow source distribution::
 
 Or with coverage::
 
-    pytest --cov PIL --cov-report term
+    pytest --cov PIL --cov Tests --cov-report term
     coverage html
     open htmlcov/index.html
diff --git a/Tests/bench_get.py b/Tests/bench_get.py
deleted file mode 100644
index 8a54ff9219c..00000000000
--- a/Tests/bench_get.py
+++ /dev/null
@@ -1,23 +0,0 @@
-import sys
-import timeit
-
-from . import helper
-
-sys.path.insert(0, ".")
-
-
-def bench(mode):
-    im = helper.hopper(mode)
-    get = im.im.getpixel
-    xy = 50, 50  # position shouldn't really matter
-    t0 = timeit.default_timer()
-    for _ in range(1000000):
-        get(xy)
-    print(mode, timeit.default_timer() - t0, "us")
-
-
-bench("L")
-bench("I")
-bench("I;16")
-bench("F")
-bench("RGB")
diff --git a/Tests/import_all.py b/Tests/import_all.py
deleted file mode 100644
index 33b07f9a25d..00000000000
--- a/Tests/import_all.py
+++ /dev/null
@@ -1,14 +0,0 @@
-import glob
-import os
-import sys
-import traceback
-
-sys.path.insert(0, ".")
-
-for file in glob.glob("src/PIL/*.py"):
-    module = os.path.basename(file)[:-3]
-    try:
-        exec("from PIL import " + module)
-    except (ImportError, SyntaxError):
-        print("===", "failed to import", module)
-        traceback.print_exc()
diff --git a/Tests/make_hash.py b/Tests/make_hash.py
deleted file mode 100644
index 7199f8c7f85..00000000000
--- a/Tests/make_hash.py
+++ /dev/null
@@ -1,66 +0,0 @@
-# brute-force search for access descriptor hash table
-
-modes = [
-    "1",
-    "L",
-    "LA",
-    "La",
-    "I",
-    "I;16",
-    "I;16L",
-    "I;16B",
-    "I;32L",
-    "I;32B",
-    "F",
-    "P",
-    "PA",
-    "RGB",
-    "RGBA",
-    "RGBa",
-    "RGBX",
-    "CMYK",
-    "YCbCr",
-    "LAB",
-    "HSV",
-]
-
-
-def hash(s, i):
-    # djb2 hash: multiply by 33 and xor character
-    for c in s:
-        i = (((i << 5) + i) ^ ord(c)) & 0xFFFFFFFF
-    return i
-
-
-def check(size, i0):
-    h = [None] * size
-    for m in modes:
-        i = hash(m, i0)
-        i = i % size
-        if h[i]:
-            return 0
-        h[i] = m
-    return h
-
-
-min_start = 0
-
-# 1) find the smallest table size with no collisions
-for min_size in range(len(modes), 16384):
-    if check(min_size, 0):
-        print(len(modes), "modes fit in", min_size, "slots")
-        break
-
-# 2) see if we can do better with a different initial value
-for i0 in range(65556):
-    for size in range(1, min_size):
-        if check(size, i0):
-            if size < min_size:
-                print(len(modes), "modes fit in", size, "slots with start", i0)
-                min_size = size
-                min_start = i0
-
-print()
-
-print("#define ACCESS_TABLE_SIZE", min_size)
-print("#define ACCESS_TABLE_HASH", min_start)
diff --git a/Tests/threaded_save.py b/Tests/threaded_save.py
deleted file mode 100644
index d47c2cf9994..00000000000
--- a/Tests/threaded_save.py
+++ /dev/null
@@ -1,57 +0,0 @@
-import io
-import queue
-import sys
-import threading
-import time
-
-from PIL import Image
-
-test_format = sys.argv[1] if len(sys.argv) > 1 else "PNG"
-
-im = Image.open("Tests/images/hopper.ppm")
-im.load()
-
-queue = queue.Queue()
-
-result = []
-
-
-class Worker(threading.Thread):
-    def run(self):
-        while True:
-            im = queue.get()
-            if im is None:
-                queue.task_done()
-                sys.stdout.write("x")
-                break
-            f = io.BytesIO()
-            im.save(f, test_format, optimize=1)
-            data = f.getvalue()
-            result.append(len(data))
-            im = Image.open(io.BytesIO(data))
-            im.load()
-            sys.stdout.write(".")
-            queue.task_done()
-
-
-t0 = time.time()
-
-threads = 20
-jobs = 100
-
-for i in range(threads):
-    w = Worker()
-    w.start()
-
-for i in range(jobs):
-    queue.put(im)
-
-for i in range(threads):
-    queue.put(None)
-
-queue.join()
-
-print()
-print(time.time() - t0)
-print(len(result), sum(result))
-print(result)
diff --git a/Tests/versions.py b/Tests/versions.py
deleted file mode 100644
index d6433b0631b..00000000000
--- a/Tests/versions.py
+++ /dev/null
@@ -1,26 +0,0 @@
-from PIL import Image
-
-
-def version(module, version):
-    v = getattr(module.core, version + "_version", None)
-    if v:
-        print(version, v)
-
-
-version(Image, "jpeglib")
-version(Image, "zlib")
-version(Image, "libtiff")
-
-try:
-    from PIL import ImageFont
-except ImportError:
-    pass
-else:
-    version(ImageFont, "freetype2")
-
-try:
-    from PIL import ImageCms
-except ImportError:
-    pass
-else:
-    version(ImageCms, "littlecms")