CAT Tourniquet "Prep", "Set Up", "Staging"... 

Here is another view showing how to "Set Up" your CAT Tourniquets from North American Rescue.
One of the issues you can run into with the Velcro on the CATs is that it gets hung up on itself; setting the TQ up this way can help with the velcro issue. In this configuration, the TQ will fit in most of the TQ holders I've used, to include TQ mounts designed for Holsters.
Note, using this method will decrease the immediate "working" diameter of the TQ, but that is an easy fix by simply undoing the velcro "handle" and extending the TQ to full length.