I have a Shinola single speed with a 38 tooth chain wheel and an 18 tooth cog. I’d like a little higher gearing so I don’t “spin out” so easily. It’s geared for 57 gear inches and I want to bump that up to the mid-60s, so I’m thinking about changing to a 15T or 16T rear cog. Should it be an even number of teeth? If I do that, should I expect to remove links from the chain or even buy a new chain? Looking at the dropout, I can slide the hub back another half inch or so.

(I’d like to avoid getting a bigger chainwheel because it might mean eliminating the chain guard, but I’d do that if it was the best option.)

Opinions?