screen, detached, stdout

Hi all,

I would like to start a series of jobs in the background and log their
stdout in specific files. The idea is to use screen for this, and I
went ahead and typed

$ screen -d -m /path/to/my/exec

which puts the job nicely in the background. Let's log stdout:

$ screen -d -m /path/to/my/exec | tee output.log

Ah, that doesn't work as the it tees the output of `screen` to the
file. Hmm.. How about

$ screen -d -m `/path/to/my/exec | tee output.log`

Now, it directs the output alright, but the session isn't detached anymore.

I don't quite understand why this happens, so if you guys have a clue
that'd be great. I'm also looking for a solution to the problem of
course.

Cheers,
Nico