Rick:
Ah -- OK, I see what you are getting at. I had two problems with this:
a) I thought NN meant linear interpolation of nearest neighbors, not simply "pick the nearest neighbor". So if it really works like you say, then that does look like a solution -- except it would be nice to know what it does in the 50/50 case.
b) ... and hence I thought you were recommending NN for the split-into-several-volumes method... which leads off to other questions.
OK, so noting Ziad's caution, basically I should investigate whether NN actually works OK.
Thanks for the correction,
Graham