I don't know what you mean by "stiffness", but I had had some difficulty shifting from 4th to 5th, and sometimes from 1st to 2nd.
I took it to my mechanic and told me off the bat that it may be the clutch. Hondas and Integras get these symptoms when something's wrong with the clutch.
It turns out that he was absolutely right. A piece of metal had broken off inside the clutch mechanism. In addition, my '97 Integra had 124,000+ miles on it.
It is now shifting very smoothly- like new!