Clematis under Weeping Bald Cypress

I got a Cascade Falls Weeping Bald Cypress (Taxodium distichum 'Cascade Falls') and want to plant a Clematis underneath it like others have done with roses. It's about six feet tall. The branches hang down to the ground. Please suggest varieties of Clematis or tell me if this is a bad idea. Thanks!

I don't know the plant you bought. Would it hang so low that the sun would be blocked from the clematis?

It might. You can trim it any length you like. It's not that thick. It's not as full as a rose bush.

Here's a link to shade tolerant clematises but keep in mind they do want sun for a few hours a day:

http://store.chalkhillclematis.com/clematisforshade.html