One observation, the NATO strop is not always standard between operators/nations. The old one that was from early 60's, used to had a loop around the loose ends of the strop, which can/could be pulled down to secure the strop (as described by snaggletooth). Similar strops down here don't always have the loop, leaving the strop quite loose around the survivor. I've given up trying to point out the "simple" solution, but one day someone will find out the hard way.
I also remember the Norwegians raised the issue of having an oversized strop available, for those "large" survivors. Around 1972 they lost a survivor from hypothermia, when it took them too long to get him out of the water because the standard strop was too short for his bulk. Slightly OT, but what the heck.