stdout/stderr to mail if error

I have searched the forum and seems like I
just don't quite find my question.

I have a script that runs out of cron and I
am trying to send normal successful stdout
to /dev/null, but if there is an error, I
want both stdout/stderr to go to mail.

In other words, I only want to know about
it if there is a problem (error), then I want
to see both stdout/stderr.

If I understand correctly, the following sends both
stdout and stderr to /dev/null:

>/dev/null 2>&1

The following sends stdout and stderr to the same place,
mail in my case.

2>&1

I guess I don't understand enough to make this happen
or even if it's possible.

Any advice is appreciated.

Thanks.

 
YOUR_SCRIPT > LOG_FILE 2>&1

This will put both stdout and stderr in LOG_FILE

direct stdout/stderr to 2 different files. If there's anything in the stderr file, send both the stdout and the stderr via email.