local and remote screens

[Rich Boyce]

Hello all,

I've just started using screen in earnest, and am very impressed. 
However, I'm currently struggling with one thing.

If I start screen on my local machine (tom), log into another (dick) 
through SSH, then detach, I cannot reattach to the session when I log 
into dick from a third machine, harry. This is because the screen 
session is actually on tom; I therefore need to log into tom in order to 
reattach. If tom is shut down, I (presumably) lose my session.

At the moment I'm not running screen on my local machine, and only on 
remote machines after SSHing in. This lets me reattach after connecting 
from a third machine. I'd like to run screen on my local machine too, 
but maintain the ability to detach/reattach on remote machines. How do 
you accomplish this? Is there a magic screen option I'm missing?

Thanks,
Rich