You can remove anything that's obviously dead, but you risk losing the plant if you cut it back hard to force new growth from near the base. On the other hand, these are not long lived plants, 15 years being a good age for a Ceanothus, so its up to you whether you take the risk or not. Should be done immediately after flowering.

I must have been very lucky with mine. I lost half of it in the frost this winter and cut it off. It now looks lopsided, a bit like one of those elegant bonsai trees, but is sending new growth out all up the trunk in an effort to fill in the gap. I wouldn't expect the new growth to flower for a long time though. You could try cutting half of yours back and if this is successful do the other half when it has recovered.

I agree with Bamboo, pruining a ceanothus is always a risk especially at that age. You would have to be prepared to loose it! I approached mine but pruning branches back to about half of where the green leaves are (start and finish) and just after flowering and gave it a spray of Maxicrop seaweed plant growth stimulant. I then do the same thing the next year and try and get it smaller that way. I have not know them to grow from branches with no green leaves on them. If you do loose it Ceanothus Concha seems to be a fast grower. It seems a habit to have lots of dead wood underneath.

Hi all, my Mum's ceanothus (small leaved) was badly damaged by frost at the end of last year, and I cut it back for her, almost to the main stem all over, and it's now shooting like mad, so it can be done. There were no leaves on the stems when I'd finished with it, either. The same thing happened to mine, only planted last year, but that also has started to shoot. However, for a really old bush, I would do what Jen H. said. It sounds good sense to me.
Good luck, anyway, Annie