Length deals with resonance, which those rings have no affect on. The rings only deal with impedance matching. If you cut the thing off, it's a "no way back" sort of thing unless you can add that cut off length back later. It's certainly possible, but not all that easy.
Resonance does make an antenna more efficient. Length is only one way of adjusting for resonance, it cant be either the 'best' way or the 'not so good' way depending on the resulting radiation pattern. for instance, a 5/8 wave antenna isn't resonant at all, all by it's self. It can be made resonant by adding the proper reactance to it, which the typical bottom coil used with them does. The radiation pattern of a 5/8 wave antenna is usually 'flatter' than others, giving a usable benefit.
- 'Doc