How can you reduce swelling in a sports injury other than using ice?

Elevation. The other way to reduce swelling is to elevate the injured part of the body. If a wrist is injured, then the wrist should be above the elbow, as well as above the heart. Fluid that collects from an injury can be absorbed by the body, but if there is excessive swelling or excessive damage, the elevation helps the body do the work.
Elevation. Sometimes massage or compression, and oral anti-inflammatories.