Gradually decreasing until little remains(adjective)
WordNet. Princeton University. 2010.
Use "tapering off" in a sentence
"Use the inverted-pyramid style of writing a resume, putting more detail at the top and tapering off at the bottom as you list your early experiences, when your jobs were certainly not as involved or eventful."
"Recovery is essential, and on three levels: micro-recovery, between sets and sessions on a given day; macro-recovery, meaning day by day and week by week; and meso-recovery—that is, the process of tapering off what I was doing as February drew near so I would peak for the Olympics."
"The level of noise from the Keep behind him was tapering off as the candlemarks passed."