How do I document code change requirements?
We have some code changes that need to be made because they were poorly written. basically, a developer looked at some old code and has found some areas of opportunity. They are going to modify the code to make it perform better. They created a project initiation document that says they are going to rewrite the code and now they want a requirements document. To me the only requirement is to streamline the code for better performance.
It seems a little over kill to try to put a requirements specification document together for this project (which has already been completed).
What do you tihnk? Any suggestions on how I should go about documenting this kind of project?

focus on test-ability
You need to write a testable requirement, that demonstrates WHAT is to be achieved.
So it could just be that "X will run 15% faster, and all functionality will still work as in blah-blah-document"
FWIW, developers who look at someone else's work will almost always find poorly-written bits that they can make much better themselves. Beware claims like this that are made just because a developer says so. Sometimes "poorly written" just means "not the way I would have done it".
I'd even go so far as to say that this is a case when requirements can stray a lot futher than usual into the "how" questions ... saying that the requirement is to make use of an index on tFoo or hash-joins when combining it with tBar gives testers a far better idea of the scope of change that they have to test.