Mythtv 720p on a 1080i difficult?

I'm considering a Mythtv setup. I have an old crt RPTV that only accepts 1080i. As a test, I installed Myth on a 2.4Ghz P4 laptop I had lying around. I played back some 1080i content OK, then tried some 720p and it really struggled. So, my question is, is it difficult to play 720p content while outputting 1080i? Also, does Myth do a good job while outputting in an interlaced mode?