I encourage my classes to hand in their homework by using homework credits.
They are given 1 credit for handing it in on time, and extra credits are given for handing in early and for work that shows extra effort. The homework I give has always got extra work that they can choose to do for extra credits. These credits are recorded on a class chart.
When the children have gained a given amount of credits, they can choose to miss the next piece of homework (to get to this total, they have invariably done more than enough to make up for this), or they can continue and save their credits.
There is a prize at the end of each half-term for the person with the most credits.