diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 00fe9f55d2..a01edb179a 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -73,8 +73,11 @@ jobs:
         env:
           LSP: '${{ matrix.lsp }}'
           LSP_EXTRACT_FILE: '${{ matrix.lsp_extract_file }}'
-          # Should match 'name:' up above
-          JOB_NAME: 'Windows (${{ matrix.python }}, ${{ matrix.arch }}${{ matrix.extra_name }})'
+      - uses: codecov/codecov-action@v3
+        with:
+          directory: empty
+          name: 'Windows (${{ matrix.python }}, ${{ matrix.arch }}${{ matrix.extra_name }})'
+          flags: Windows,${{ matrix.python }}
 
   Ubuntu:
     name: 'Ubuntu (${{ matrix.python }}${{ matrix.extra_name }})'
@@ -119,8 +122,11 @@ jobs:
         run: ./ci.sh
         env:
           CHECK_FORMATTING: '${{ matrix.check_formatting }}'
-          # Should match 'name:' up above
-          JOB_NAME: 'Ubuntu (${{ matrix.python }}${{ matrix.extra_name }})'
+      - uses: codecov/codecov-action@v3
+        with:
+          directory: empty
+          name: 'Ubuntu (${{ matrix.python }}${{ matrix.extra_name }})'
+          flags: Ubuntu,${{ matrix.python }}
 
   macOS:
     name: 'macOS (${{ matrix.python }})'
@@ -150,9 +156,11 @@ jobs:
           cache-dependency-path: test-requirements.txt
       - name: Run tests
         run: ./ci.sh
-        env:
-          # Should match 'name:' up above
-          JOB_NAME: 'macOS (${{ matrix.python }})'
+      - uses: codecov/codecov-action@v3
+        with:
+          directory: empty
+          name: 'macOS (${{ matrix.python }})'
+          flags: macOS,${{ matrix.python }}
 
   # https://github.com/marketplace/actions/alls-green#why
   check:  # This job does nothing and is only used for the branch protection
diff --git a/ci.sh b/ci.sh
index 3cd78cfb18..875d778487 100755
--- a/ci.sh
+++ b/ci.sh
@@ -6,10 +6,6 @@ set -ex -o pipefail
 uname -a
 env | sort
 
-if [ "$JOB_NAME" = "" ]; then
-    JOB_NAME="${TRAVIS_OS_NAME}-${TRAVIS_PYTHON_VERSION:-unknown}"
-fi
-
 # Curl's built-in retry system is not very robust; it gives up on lots of
 # network errors that we want to retry on. Wget might work better, but it's
 # not installed on azure pipelines's windows boxes. So... let's try some good
@@ -102,12 +98,8 @@ else
 
     INSTALLDIR=$(python -c "import os, trio; print(os.path.dirname(trio.__file__))")
     cp ../pyproject.toml $INSTALLDIR
-    # We have to copy .coveragerc into this directory, rather than passing
-    # --cov-config=../.coveragerc to pytest, because codecov.sh will run
-    # 'coverage xml' to generate the report that it uses, and that will only
-    # apply the ignore patterns in the current directory's .coveragerc.
-    cp ../.coveragerc .
-    if pytest -r a -p trio._tests.pytest_plugin --junitxml=../test-results.xml --run-slow ${INSTALLDIR} --cov="$INSTALLDIR" --verbose; then
+
+    if pytest -r a -p trio._tests.pytest_plugin --junitxml=../test-results.xml --run-slow ${INSTALLDIR} --cov="$INSTALLDIR" --cov-report=xml --verbose; then
         PASSED=true
     else
         PASSED=false
@@ -119,13 +111,5 @@ else
         netsh winsock reset
     fi
 
-    # The codecov docs recommend something like 'bash <(curl ...)' to pipe the
-    # script directly into bash as its being downloaded. But, the codecov
-    # server is flaky, so we instead save to a temp file with retries, and
-    # wait until we've successfully fetched the whole script before trying to
-    # run it.
-    curl-harder -o codecov.sh https://codecov.io/bash
-    bash codecov.sh -n "${JOB_NAME}"
-
     $PASSED
 fi