In this video I show a variation the Cross Collar Choke with the arms being completely straight. There are a lot of different ways to do a cross collar choke, and I personally use a lot of different methods. This is one of my favorite ways to do the Cross Collar Choke as it doesnt burn my grips and it's highly effective.
Notice the head placement on the mat. Correct basing on the hairline is extremely important, both for safety AND effectiveness. This will take some getting used to as we have been conditioned to maintain weight on our butt in mount rather than our hips and abdominal muscles.
Try it out and let me know what you think.