How to divide old Cymbidiums?

[JanS]

I have a number of Cymbidiums, all descendants from a plant given to me some 15 years ago. They do pretty well, put out new growth each year and most just finished flowering, some with 2 flower spikes.

When they get too big for a reasonably sized pot, I divide them into two but have been leaving the old (but still live, leafless) bulbs attached. I have to say, this makes the plants not very appealing. I have been afraid to cut all the leafless bulbs off (that still have good live roots in many cases) for fear of cutting stored nutrition off from the two or so newest growths that would be left. Yet, Cyms for sale never seem to have any leafless bulbs...

I am interested in what the rest of you would do with my plants - photos of two typical ones are attached.

Thanks!