If you make substantial modifications to the code, its probably a good idea to add your copyright under the original author's.
Something like this should suffice (even if you put it just under the original license):
/*
* Copyright (C) 2009 (your name here)
*
* - Extended foo for bar
* - Optimized foobar()
* - Added handler raboof for reversing multibyte strings
* - Program is now sentient, keep away from children
*/
Keep in mind that the 3 clause BSD is one of the most permissive licenses used today. It also happens to be my license of choice for most things that I release to the public. Most people who release code using it are pretty laid back.
Don't be too paranoid, just show a good faith attempt to detail how your version is different from the original, just so its not confused by someone as being the original.