OK, to wrap up.....
I have a horse, tail at the rear docked - TIPSTER? If 'Rear' is STER(n) -'Tail Docked' where does 'Tip' come from?
Like old TV stories on the box, around for all to see - ANALOGUE Why 'Stories on the box'?
Flower quicker to dead-head - ASTER Is it 'Faster' without the 'Head'?