v.1. To reduce the size of some piece of wood by cutting small bits or paring shavings: I whittled down the pencil's tip to expose more lead. I bit nervously on my pencil until I had whittled it down to nothing.
2. To reduce something gradually, as if by whittling with a knife: The couple whittled down their debt by making small payments. We whittled the other team's lead down to one point with a series of small gains.