git config --global alias.add-commit '!git add -A && git commit'
After this, you can simply check in all new, modified, and deleted files with a simple
git add-commit -m 'My commit message'
I have aliased this command also to
git ac in order to save further on typing. I never thought that this combination could be that useful, but actually I think it really is. Thanks to the questioner for bringing the idea up.