diff --git a/.travis.yml b/.travis.yml
index fe7acec0..6e9403cc 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -5,6 +5,10 @@ language: python
 
 matrix:
   include:
+    - python: "3.8"
+      env: TOXENV=flake8
+    - python: "3.8"
+      env: TOXENV=mypy
     - python: "2.7"
       env: TOXENV=test-py27,codecov
     - python: "3.4"
diff --git a/src/hyperlink/_url.py b/src/hyperlink/_url.py
index 15f6cc9d..f39525d3 100644
--- a/src/hyperlink/_url.py
+++ b/src/hyperlink/_url.py
@@ -97,7 +97,7 @@ def __repr__(self):
         if var_name:
             # superclass type hints don't allow str return type, but it is
             # allowed in the docs, hence the ignore[override] below
-            def __reduce__(self):  # type: ignore[override]
+            def __reduce__(self):
                 # type: () -> str
                 return self.var_name
 
@@ -448,7 +448,7 @@ def _optional(argument, default):
 
 
 def _typecheck(name, value, *types):
-    # type: (Text, T, Type) -> T
+    # type: (Text, T, Type[Any]) -> T
     """
     Check that the given *value* is one of the given *types*, or raise an
     exception describing the problem using *name*.
@@ -479,7 +479,7 @@ def _textcheck(name, value, delims=frozenset(), nullable=False):
 
 
 def iter_pairs(iterable):
-    # type: (Iterable) -> Iterator
+    # type: (Iterable[Any]) -> Iterator[Any]
     """
     Iterate over the (key, value) pairs in ``iterable``.
 
diff --git a/src/hyperlink/test/common.py b/src/hyperlink/test/common.py
index a2961f45..f489266e 100644
--- a/src/hyperlink/test/common.py
+++ b/src/hyperlink/test/common.py
@@ -7,9 +7,13 @@ class HyperlinkTestCase(TestCase):
     assertRaises method for Python 2.6 testing.
     """
     def assertRaises(  # type: ignore[override]
-        self, expected_exception, callableObj=None, *args, **kwargs
+        self,
+        expected_exception,  # type: Type[BaseException]
+        callableObj=None,    # type: Optional[Callable[..., Any]]
+        *args,               # type: Any
+        **kwargs             # type: Any
     ):
-        # type: (Type[BaseException], Optional[Callable], Any, Any) -> Any
+        # type: (...) -> Any
         """Fail unless an exception of class expected_exception is raised
            by callableObj when invoked with arguments args and keyword
            arguments kwargs. If a different type of exception is
diff --git a/src/hyperlink/test/test_url.py b/src/hyperlink/test/test_url.py
index dd554fa5..fa5c7bf1 100644
--- a/src/hyperlink/test/test_url.py
+++ b/src/hyperlink/test/test_url.py
@@ -1112,7 +1112,6 @@ def test_autorooted(self):
 
         attempt_unrooted_absolute = URL(host="foo", path=['bar'], rooted=False)
         normal_absolute = URL(host="foo", path=["bar"])
-        attempted_rooted_replacement = normal_absolute.replace(rooted=True)
         self.assertEqual(attempt_unrooted_absolute, normal_absolute)
         self.assertEqual(normal_absolute.rooted, True)
         self.assertEqual(attempt_unrooted_absolute.rooted, True)
diff --git a/tox.ini b/tox.ini
index eb2f07be..bfd3c7b4 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,7 +1,7 @@
 [tox]
 
 envlist =
-    flake8
+    flake8, mypy
     test-py{26,27,34,35,36,37,38,py,py3}
     coverage_report
     packaging
@@ -55,6 +55,8 @@ passenv =
 setenv =
     PY_MODULE=hyperlink
 
+    test: PYTHONPYCACHEPREFIX={envtmpdir}/pycache
+
     test: COVERAGE_FILE={toxworkdir}/coverage.{envname}
     {coverage_report,codecov}: COVERAGE_FILE={toxworkdir}/coverage
     codecov: COVERAGE_XML={envlogdir}/coverage_report.xml
@@ -75,12 +77,9 @@ basepython = python3.8
 
 skip_install = True
 
-# Pin pydocstyle to version 3: see https://gitlab.com/pycqa/flake8-docstrings/issues/36
 deps =
     flake8-bugbear==19.8.0
-    #flake8-docstrings==1.4.0
-    #flake8-import-order==0.18.1
-    #flake8-pep3101==1.2.1
+    #flake8-docstrings==1.5.0
     flake8==3.7.9
     mccabe==0.6.1
     pep8-naming==0.9.1
@@ -142,11 +141,9 @@ basepython = python3.8
 
 skip_install = True
 
-
 deps =
     mypy==0.750
 
-
 commands =
     mypy                                       \
         --config-file="{toxinidir}/tox.ini"    \
@@ -173,7 +170,11 @@ warn_return_any          = True
 warn_unreachable         = True
 warn_unused_ignores      = True
 
+[mypy-hyperlink._url]
 # Don't complain about dependencies known to lack type hints
+# 4 at time of writing (2020-20-01), so maybe disable this soon
+allow_untyped_defs = True
+
 
 [mypy-idna]
 ignore_missing_imports = True
@@ -196,8 +197,8 @@ deps =
 
 commands =
     coverage combine
-    coverage report
-    coverage html
+    - coverage report
+    - coverage html
 
 
 ##
@@ -217,6 +218,8 @@ deps =
     codecov==2.0.15
 
 commands =
+    # Note documentation for CI variables in default environment's passenv
+
     coverage combine
     coverage xml -o "{env:COVERAGE_XML}"
     codecov --file="{env:COVERAGE_XML}" --env                 \
@@ -281,7 +284,9 @@ basepython = python
 deps =
    check-manifest==0.40
    readme_renderer==24.0
+   twine==2.0.0
 
 commands =
    check-manifest
-   python setup.py check --metadata --restructuredtext --strict
+   pip wheel --wheel-dir "{envtmpdir}/dist" --no-deps {toxinidir}
+   twine check "{envtmpdir}/dist/"*