Are there any narcotic painkillers that do not cause constipation?

I'm having surgery in August and at my pre-op appointment my surgeon will write scrips for post-op painkillers and I'm wondering if any of them DON'T cause constipation. The last thing I want to be is recovering and constipated. When I had my wisdom teeth removed I was prescribed something with codeine and for that reason I took a total of about 1.5 pills, however I was never in that much pain for that. But if something is available that won't cause constipation, I want to ask for that. Any advice?