I don't mind the compressing at all, I just wish it would not do it

every time I move a message, and more importantly: can I somehow push

that message to the background so I can keep it out of sight?

 The compressing of a folder is a critical task and if something happens in the process then it's easy to lose a whole mail folder.  That's why the process is a foreground process.  You really should not be doing anything else until this process is finished.

You can though make this a manual operation or increase the total size that triggers the compression using Tools | Options | Advanced Settings | Deleted space recovery 

When you delete a message, Pegasus Mail does not actually remove the message's data from the folder - instead, it simply marks the message as "deleted", and adds the size of the message data to an internal counter. Whenever the folder is closed, Pegasus Mail checks the internal counter to see if it exceeds a particular size, and if it does, it recovers the space occupied by all the deleted messages in the folder. If the folder is very large, or if you delete information from it frequently, this process of compression may become annoying or may take too long. Changing the value of this control allows you to tune the point at which Pegasus Mail will perform the deleted space recovery operation - setting a large number will make the operation happen less frequently, at the cost of having some of your disk space occupied by "dead" data. Setting this field to 0 turns off deleted space recovery - deleted data will never be removed from the folder, and it will therefore continue to get larger and larger over time. You can manually compress the folder via the right click though.
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I often receive emails with large attachments. This is not a problem in itself but when I move an e-mail like this between folders and then switch to a different folder Pmail decides to compress that folder. That means that for more than a minute I've got the 'Compressing folder...' message in the middle of the screen and I cannot get another window to cover it, essentially blocking me from doing anything else until it is done.

I don't mind the compressing at all, I just wish it would not do it every time I move a message, and more importantly: can I somehow push that message to the background so I can keep it out of sight?