Wooo..tricky
This should be a straightforward process but - due to constraints in time and budget - the ability to model the business is not always possible. Therefore, you may have to take it from scratch..... The first thing I like to do is develop a "Systems Analysis" estimate in Excel that lays out all your assumptions as well as rough sizings / functional area. Present this to your PM and have THEM prioritize ( with the client's help) what areas to analyze first
Assuming you have requirements that were handed to you I would (personally)
1. Talk to the Project Manager and find out what the deadline is to have "developer ready" artifacts
1a> Validate with the developers exactly what these artifacts are?? Is it ONLY use cases or do they expect more stuff? Where is the line between you and the coders?
1b. UPDATE YOUR SIZING ACCORDINGLY
2. validate there is money to actually BUILD something (again from the PM)
3. Have an open session with real end users to validate which of the requirements are the most important ( what is their "wish list")
3a> Now that you have their "optimal list" , ask them what they are willing to sacrifice if "push comes to shove" budget-wise
3b> Assuming this is a Rebuild ( and not a new system) ask them what functionality must not be lost!!!
4. Now that you have prioritized requirements, it'll be important to figure out what the use cases should be. In geert's example ( and my current situation) I am using business process models to identify means of automation. These points in the process model will now link to a System Use Case
If this is not possible, ask the PM and/or steering committee what their functionality priorities are whilst highlighting to them what the users brought up.
5. Now that you ahve Management and User priorities, start scratching out User Interface prototypes. You can do this by looking at an OLD system / observing users OR start from scratch.
6. In looking at the UIs, you will find users can perform functions (add, delete, modifies) which should be captured in System Use Cases.
7. Develop those Use Cases which are in the "areas of priority" and link any user requirements to them ( so none get lost).
8. Develop any supporting artifacts that the coders indicated that they needed.
9. Keep everyone in the loop on progress and risks
Have fun!

p.s. bruce is not far off the mark in several of his observations!!!