Thanks. FWIW the antenna is a Thunderpole Orbitor 1.5m (http://www.thunderpole.co.uk/large-cb-a ... bitor.html
). I spoke to the chap who designed it, and I sort-of got the impression that high SWRs in the upper channels were not entirely unusual. One of his colleagues said, essentially, if the SWR is < 3, just disconnect the bloody meter and stop obsessing about it. However, it bugs me, not knowing what the problem is.
The SWR varies more-or-less linearly across the channel range, so 1.5 on ch.1,then 2.0 on ch. 20, ~3 on ch. 40. An adjustment of an inch or so in length does not affect this pattern significantly. The designer said that if removing an inch from the length does not help, it probably wouldn't help to shorten it any more. However, I can get an SWR or 1.5 on ch. 40 by removing the whip from the coil, and replacing it with two feet of copper wire. So my gut feeling is that the proper antenna could produce better SWR in the higher channels if it wanted to -- but, of course, that might well be at the expense of worse SWR elsewhere.
I've checked for obvious faults -- there is DC continuity everywhere there should be, and nowhere there shouldn't. Arguably powering the radio from a cigar lighter socket is non-ideal, but it's designed to be used that way.
If the roof bar isn't much of a ground plane, then the nearest potential ground plane is the car roof, which is about 6" below the antenna coil, and 12" below the whip. Maybe this is non-ideal? There's a six-inch tall grounded metal stalk very close the antenna coil -- it is where my emergency beacon attaches. I accept that this might also be a problem, although for various reasons I can't do much about it.
If I've just got to live with this situation, then fair enough. What worries me, though, is that something might actually be faulty, and I just can't figure out what.