No need to go to the boat Terry. If you have a piece of line handy, you can just pretend that it is spliced and show us the half-twist. Or how you put the half-twist in the loop.
Hi Brian, imagine, if you will, that the line in the pictures below is three strand. Rather than beginning the splice as you normally would with the working and bitter end laying naturally, I start the splice 180 degrees from the normal position. That places a twist in the eye. The eye remains the same size, except you have to untwist the eye to mount it on the cleat.
What I do is unlay the bitter end to the length I want and where I have placed a piece of electrical tape to prevent further unlaying. That tape is my splice start point.
In the picture below imagine that the line is un-layed to the tape, I then place the taped part of the line underneath the working end by 180 degrees and start my splice there. As you can see that places a twist in the eye, making it smaller in size while on the cleat, thus helping to prevent it from coming off. The eye is still the same size in diameter, but the twist makes the loop part smaller. I hope this helps.
There is a simple technique that I use for mounting and dismounting the twisted eye from the cleat rather than actually opening the eye, and that is to swing the eye from side to side letting the cleat horn slide through the eye twist.
A short video clip will help answer questions and I will do that the next time to the boat. As they say a picture is worth a thousand words.