I have a Butternut HF6V which is a 10m-80m vertical. I travel full time in my RV and needed to be able to quickly set up and take down. I built a wooden tilt base and mounted 16 each 25 foot metal tape measures around the 18" diameter base, tying them with a copper wire around the base. I set them at 22 degrees apart. I can pull the tapes out, lock them and bang, 16 each 25 foot radials.
Using this ground radial setup the Butternut on 80m had a very narrow bandwidth, about 25-20 kHZ which indicates a decent ground. With a poor ground, the bandwidth on 80m would be much wider which would indicate a poor or lossy ground plane (ie the dummy load theory).
With only 15 feet to run radials, I would run as many as you can reasonably (say 25-30) and you should do as well as possible.
I think the bigger issue is the poor antenna efficiency with a short vertical. Phil Silas ( www.ad5x.com
) has a number of very good articles on the 43 foot vertical where he compares this to a short (23 foot) antenna. The smaller vertials are not too bad from 10m to 20m but on 40m and lower frequencies the antenna efficiency is lower than 50%.
ALL antennas are a compromise unless you have the space to put a 1/2 wave dipole up at least 1/2 wavelength.
As said earlier in this thread, you do the best you can technically and enjoy the result.
If you are looking to do something on say 20m, look into a Petlowany counterpoise similar to the taktenna concept.http://www.n0lx.com/petlowany_ground.html