1
general::
1. Become thinner or narrower at one end, as in The road began to taper off until it was just a narrow path. [c. 1600] 2. Diminish or lessen gradually, end by degrees, as in The storm finally tapered off. [Mid-1800s]
American Heritage Idioms
2
general::
Phrase(s): taper off (doing something)
gradually to stop doing something; to do less and less of something until there is no more to do. • Bob tried to taper off smoking again. • I can’t taper off overeating. I have to stop all at once by going on a strict diet.
McGrawhill's American Idioms And Phrasal Verbs