I had the same problem. I recently began riding again after a long hiatus, and soon realized my old 6-speed 12-21t freewheel was not going to cut it. When I was riding junior races in the mid-80s, the low gear restrictions were about 50x15t (varied slightly with age group) and it was not uncommon to see 15t-20t or 16t-21t straightblocks, which I always thought looked kind of strange.

You can try to find replacement cogs, though they are hard to come by. I bought a couple replacement cogs from Ebay seller "Everything Bicycles 1959". You might also consider a Shimano HyperGlide freewheel. They are pretty cheap (less than $30), come in 6- or 7-speeds, and people swear by them.

EDIT: If you do try to replace some cogs, this compatibility chart may help.