diff --git a/.travis.yml b/.travis.yml
index 067ee373..4bd7d724 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -84,7 +84,10 @@ env:
 
 install:
   - pip install "pip>=7.1.0"
-  - pip install tox-travis tox codecov coverage
+  - pip install tox-travis tox codecov
+  # Coverage 5.0+ has issues similar to:
+  #   https://github.com/nedbat/coveragepy/issues/915
+  - pip install "coverage<5.0"
 
 script: CFLAGS="$CFLAGS_warnings $CFLAGS_std" tox
 
diff --git a/tox.ini b/tox.ini
index 92933b84..2faa94d0 100644
--- a/tox.ini
+++ b/tox.ini
@@ -9,7 +9,9 @@ envlist = py27,py34,py35,py36,py37,py38,py39,{py2,py3}-nosasltls,doc,py3-trace,c
 minver = 1.8
 
 [testenv]
-deps = coverage
+# Coverage 5.0+ has issues similar to:
+#   https://github.com/nedbat/coveragepy/issues/915
+deps = coverage<5.0
 passenv = WITH_GCOV
 # - Enable BytesWarning
 # - Turn all warnings into exceptions.
@@ -75,7 +77,9 @@ deps = {[testenv:pypy]deps}
 commands = {[testenv:pypy]commands}
 
 [testenv:coverage-report]
-deps = coverage
+# Coverage 5.0+ has issues similar to:
+#   https://github.com/nedbat/coveragepy/issues/915
+deps = coverage<5.0
 skip_install = true
 commands =
     {envpython} -m coverage combine