I can honestly say that C++ exceptions have never, in decades, cost me a single hour's lost sleep. If you have any trouble with them, I promise that you are Doing It Wrong. You can tell you are Doing It Wrong if it is not super-easy and super-clean.

The key is to make sure all your cleanup code is in destructors where it will be exercised frequently as part of the normal operation of your program. In the event an exception is thrown, a bunch of destructors run, as usual, and your program ends up in a known clean state, with no extra effort.