diff --git a/appveyor.yml b/appveyor.yml
index 5317d989c7..cf5a653592 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -27,5 +27,4 @@ test_script:
   - "python -c \"import os, trio; print(os.path.dirname(trio.__file__))\""
   # -u makes sure we get prompt output
   - "python -u -m pytest -W error -ra --run-slow --faulthandler-timeout=60 ../trio -v -s --cov=trio --cov-config=../.coveragerc"
-  - "coverage combine"
   - "codecov"
diff --git a/ci/travis.sh b/ci/travis.sh
index 3ec2fb75e4..8978d448cd 100755
--- a/ci/travis.sh
+++ b/ci/travis.sh
@@ -95,6 +95,5 @@ else
     INSTALLDIR=$(python -c "import os, trio; print(os.path.dirname(trio.__file__))")
     pytest -W error -ra --run-slow --faulthandler-timeout=60 ${INSTALLDIR} --cov="$INSTALLDIR" --cov-config=../.coveragerc --verbose
 
-    coverage combine
     bash <(curl -s https://codecov.io/bash)
 fi
diff --git a/test-requirements.txt b/test-requirements.txt
index 4548fc2dd0..11feb20813 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -1,5 +1,5 @@
 pytest >= 3.3  # for catchlog fixture
-pytest-cov
+pytest-cov >= 2.6.0
 ipython        # for the IPython traceback integration tests
 pyOpenSSL      # for the ssl tests
 trustme        # for the ssl tests