diff --git a/.github/workflows/appimage.yml b/.github/workflows/appimage.yml
index a196802..7df7071 100644
--- a/.github/workflows/appimage.yml
+++ b/.github/workflows/appimage.yml
@@ -15,16 +15,22 @@ jobs:
         image: ['1', '2010', '2014']
         arch: [x86_64, i686]
         tag: [cp27-cp27m, cp27-cp27mu, cp35-cp35m, cp36-cp36m, cp37-cp37m,
-              cp38-cp38, cp39-cp39]
+              cp38-cp38, cp39-cp39, cp310-cp310]
         exclude:
+          - image: '1'
+            tag: cp310-cp310
           - image: '2010'
             tag: cp27-cp27m
           - image: '2010'
             tag: cp27-cp27mu
+          - image: '2010'
+            tag: cp35-cp35m
           - image: '2014'
             tag: cp27-cp27m
           - image: '2014'
             tag: cp27-cp27mu
+          - image: '2014'
+            tag: cp35-cp35m
 
     steps:
     - uses: actions/checkout@v2
@@ -62,7 +68,7 @@ jobs:
     if: github.ref == 'refs/heads/master'
     strategy:
       matrix:
-        version: [2.7, 3.5, 3.6, 3.7, 3.8, 3.9]
+        version: ['2.7', '3.5', '3.6', '3.7', '3.8', '3.9', '3.10']
 
     steps:
     - uses: actions/download-artifact@v1
diff --git a/README.md b/README.md
index 8f6afe2..fdd17fb 100644
--- a/README.md
+++ b/README.md
@@ -15,10 +15,10 @@ single file and changing its mode to executable, e.g.  as:
 
 ```sh
 wget https://github.com/niess/python-appimage/releases/download/\
-python3.9/python3.9.1-cp39-cp39-manylinux1_x86_64.AppImage
-chmod +x python3.9.1-cp39-cp39-manylinux1_x86_64.AppImage
+python3.9/python3.9.4-cp39-cp39-manylinux1_x86_64.AppImage
+chmod +x python3.9.4-cp39-cp39-manylinux1_x86_64.AppImage
 
-./python3.9.1-cp39-cp39-manylinux1_x86_64.AppImage
+./python3.9.4-cp39-cp39-manylinux1_x86_64.AppImage
 ```
 
 This should start a Python 3.8 interactive session on _almost_ any Linux
@@ -30,9 +30,9 @@ its standard library.  However, if you plan to install extra packages we
 recommend extracting the AppImage, e.g. as:
 
 ```sh
-./python3.9.1-cp39-cp39-manylinux1_x86_64.AppImage --appimage-extract
+./python3.9.4-cp39-cp39-manylinux1_x86_64.AppImage --appimage-extract
 mv squashfs-root python3.9
-rm -f python3.9.1-cp39-cp39-manylinux1_x86_64.AppImage
+rm -f python3.9.4-cp39-cp39-manylinux1_x86_64.AppImage
 
 export PATH="$(pwd)/python3.9/usr/bin:$PATH"
 ```