General :: Bash Command History Update Before Execution Of Command

Bash's command history is great, especially it is useful when adding the history -a command to the COMMAND_PROMPT.However, I'm wondering if there is a way to log the commands to a file as soon as the Return key is pressed, e.g. before starting the command and not on completion of the command (using the COMMAND_PROMPT option would save the command once the prompt is there again).

I read about auditing programs like snoopy and session recorder like script but I thought they're already too complex for the simple question I have. I guess that deactivating that script logs all the output of the command would lead already in the right direction but isn't there a quicker way to solve that probelm?