How many speeds? Indexed or friction?

I'm cheap, and use the HKK Z-Chains. I had a similar problem with the lower gears (high tooth-count) on a Miyata 210. Replacing the existing chain with a Z-Chain helped a lot, but the problem didn't go away until I replaced the 5 speed Sun Tour freewheel with a 6 speed (seems counter-intuitive doesn't it?) Shimano freewheel.