Taper off
Definition 1 of 2
Pro Tip 1/3Subtle Decrease
Use 'taper off' to suggest a smooth, gradual reduction rather than an abrupt stop. 
The chatter in the audience tapered off as the lights dimmed.
Pro Tip 2/3Natural Phenomena
'Taper off' is often used to describe natural events that slowly come to an end. 
As night approached, the wind started to taper off.
Pro Tip 3/3Expectations
When something 'tapers off', it often implies a predictable decline in activity or interest. 
After the holiday season, gift sales began to taper off.