Pain in the elbows while doing tricep extensions

So I was doing tricep extensions on a pull down machine like this guy:

The problem with this is the elbows are the weakest link in this movement, so they are taking the brunt of abuse.  If you look at how this guy is doing it, the elbows are the only stabilizers. They're providing the balance in the movement and preventing this guy's body from moving around.  This means they are put into a susceptible position that could lead to elbow injury.

How do you remedy this?  Do tricep extensions using a barbell loaded with weights while laying your back on a flat bench.  If you want to use a pull down machine like the guy above, use a machine that has a back pad so that you can use the back pad to stabilize your body while in the range of motion. Or go on a machine like the one below:

 The main point of this post is if you're going to do tricep work, do it in a safe stabilized position not like the guy in the first video at the top in a unstabilized standing position.