allow a very small margin of something usually time
RELATED IDIOMS :
fine feathers :
The proverb fine feathers make fine birds meaning that an eye-catching appearance makes a person seem beautiful or impressive has been known in England since the late 19th century. It is recorded in the early 16th century in French as les belles plumes font les beaux oiseaux.
not to put too fine a point on it :
to speak bluntly
one fine day :
at some unspecified or unknown time
1990 - Wilfred Sheed - Essays in Disguise - If Sydney blew away one fine day, Melbourne could easily take its place as a center of mateship and conspicuous democracy.