My team started with RUP with extensive mentoring from Rational. We did a standard waterfall style with requirements gathering, use cases, design, construction, etc. for several years.
We found we were dealing with overly large chunks of work, and recently shifted to an iterative development style with planning and tracking at story levels, like most agile methods. This is not a rejection of RUP; it is a legitimate customization of RUP.
We still do our use cases, but we build them up one story at a time. We use Rational tools to connect use cases to a requirements matrix, and requirements design docs and everything else we do.
Here's some info on our
Story Driven Process.