Ice-packs on sports injuries - why?

What is the benefit of applying ice-packs to sports injuries? I know it stops swelling, I imagine by constricting the arteries, but presumably the swelling occurs for a good reason, so why would you want to inhibit it?

Actually, it’s part of the ICE procedure: ice, compression, elevation.

The actual swelling often means body fluids infiltrating tissues. In some ways, it’s the body’s response to creating its own splint and reduce further injury. OTOH, for healing to begin, the swelling must be reduced to allow joint mobility and rehab. This means the healing and rehab process are delayed, meaning it will take longer to return to the action.

By applying ICE, you reduce the amount of swelling and thus reduce the time for healing to begin.

I thought it was RICE - Rest, ice compression, elevation - or has that changed since I was in jr. high basketball?