How to change the output redirection of a running process?

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http://unix.stackexchange.com – I know how to redirect output and how to suppress them in bash. Now, suppose I accidentally forgot to append the output redirection part to the command (e.g. 2>&1 or > /tmp/mystdout) and my background process is already running for a while, can I still change to where stdout and stderr are being written to? I really would like not to kill and restart the application. To be more specific as asked by Gilles in his comment, I would like to fiddle with it in these scenarios in specific: wrong output file forgot to redirect stderr to stdout or a combination of both E.g. I have Apach (HowTos)