I also have a p2040 and the case everyone uses for this is the CaseLogic playstation bag.
I have two of them. I bought one for $5 US on ebay and the other for about $15 US at compusa.
Everyone has them for the P as it is perfect.
(also fits the new p5000 series apparently)
And it just happens to fit the Tr1 perfectly also.
It is very light, small, padded, and it has a adapter pouch on the side that holds the adapter and has room for other stuff. It has a shoulder strap.
I’m a little suprised that I haven’t heard it mentioned here.
Here’s a link (a reference for P owners)
http://www.pooterland.com/caselogic.html
Look at all the stuff this guy puts in it. And even with all this it’s low profile.
I just keep the adapter and and usally the novel i’m reading on the plane so that this is all I carry on.
The Sony case that’s around 60-100US is a slip for a larger bag which looks great and I want it but maybe n ot for $100US . That other case that I see mentioned on this forum that sells for a whopping $250Us
Looks so so.