If you’re playing underwater rugby or football, how do you keep the ball from floating or sinking?

I just found out that people like to play football and rugby underwater. The submarine versions of these ball sports require three-dimensional tactics: not only are you throwing or passing the ball left or right, forward or backward, you may also be sending it down or up. If you approach these games like you would their dry-land equivalents you’re missing some tricks. (To borrow a quotation from Spock in Star Trek II, “He is intelligent, but not experienced. His pattern indicates two-dimensional thinking.”)
Of course, for this tactical point to make sense, you have to be able to throw the ball underwater. Regular balls are buoyant, so as soon as you let them go they’ll just float to the surface. The balls used in underwater football and underwater rugby are filled with salt water. This makes them negatively buoyant. In a fresh water pool, they do not float to the surface. Instead, they sink… very slowly. You can throw them underwater some short distance (a couple of metres if you’re strong enough), making these games possible and slightly less of a very soggy wrestling match.
(Side note: I have heard rumours that some people are also negatively buoyant. They have low body fat and small frames and therefore don’t naturally float. I have no idea if this is true or not.)
In contrast, underwater hockey does not use a negatively buoyant puck. Instead, it’s made of lead and sinks right to the bottom of the pool. The cruel part is that players have to hold their breath or they can’t get anywhere near the puck. Even more extreme is underwater ice hockey. That uses a floating puck, and the game is played upside down on the underside of the pool’s frozen surface.