I've got a 15 year old Kohler 2 handle kitchen sink that's leaking around spout base. I took the spout off and there's a valve looking thing loose up in the handle. It appears that it once screwed into the base of the faucet assy (the water pressure has always been bad at this sink). It looks like you need to take out a brass inner sleeve (like a short piece of thick pipe with half the diameter cut off just at the end). Is there a special tool to get this thing out? Or is there some sort of split ring on the back side of the rubber sealing o - ring?

I wish I could help you but with your information it is almost impossible. How did you get the spout off the faucet. You say that there is a valve looking thing loose in the handle, is this still part of the spout? Is the spout an open tube? Do you hae a separate spray beside your faucet? Give me more info and maybe I can help.

Yes, there's a separate plastic sprayer. I disconnected the spout from the base unit with a small monkey wrench. This chrome screw piece somehow attaches to the back of the spout (and allows the spout to swing from side to side). Looking inside the screw piece is the brass unit that I referred to. It's between the brass piece and the tube of the spout that this rubber valve screw is located (loose). If the passageway in the spout had sufficient diameter, I could shake the rubber screw out the faucet end.

Order: hot and cold water pipes to base unit, base unit to chrome screw piece (inside is brass pipe thing), chrome screw piece (that allows spout to swing) to back of spout and finally spout to faucet end (with the rubber screw rattling and stuck back at the back of spout).