My answer was real but it had some comedic elements because you called it a "fixie" which I have to keep deleting and re-writing because it doesn't believe it is a word either and you also claimed that a fixed gear bicycle goes through more stress somehow. If a part is broken don't use it, simple as that. Also as stated earlier don't use carbon bars if you are unsure of them. No point in riding being nervous all the time that your bars will break just to save a smidgen of weight and get a possible small bit of added comfort. The seat posts and stems and such I listed are all perfect ways to add comfort.

As far as brake levers, go out and get yourself some SRAM S-500 levers and be happy, they are extremely comfortable and urklenomically designed and will work fine on a carbon bar and won't have the issues of the bolt digging into the bar as others mentioned. Yeah they do cost money but for a nice place to keep your hands a nice functional piece of equipment that allows you to slow down or stop, they are worth it. I have had them on 3 bikes and will continue using them till Shimano comes out with something similar or better in the ergo department.