c. 1600, "epicurean, having delicate tastes," from fine (adj.) + toothed "having teeth" (of a certain kind); see tooth (n.). By 1703 as "having fine teeth" (of a saw, file, comb, etc.); fine-tooth in this sense attested from 1804.
a fine-toothed comb
fine
finely
fineness
finery
finesse
fine-toothed
fine-tune
finger
finger-board
fingering
fingerless