In my last entry, I mentioned that it should be possible to implement user stories within a short period of time. But then I asked, "[A]long what lines to you divide the user stories so that they are each sufficiently small?"
You have two alternatives.
One alternative is shorten the development effort by abbreviating the "span" of the story. Take a word processor as an example. Instead of a story encompassing the entire process of creating a new document, composing and editing its contents, saving it, and printing it, you might pick just one step. You might, for instance, choose composing the document as the user story, and leave out the creation of a new document, saving it, and printing it. I generally don't recommend this approach.
The approach I usually recommend is to maintain the "span" of the story, but simplify some of the steps in it. For example, still implement the functionality to create, compose, save, and print, but make it so that the user only types raw text and cannot do any formatting.
It really doesn't matter much whether they are "user stories" or "use cases", you still can reduce the level of effort so that it is possible to implement them in a single iteration. I mentioned some of the approaches in an entry in August.