I'm a big fan of DDs now having cut my teeth on concentrics over the years. For sure a *good quality* DD will give better left/right separation from shallow to deep IMO. Unfortanetly there are no DDs that I know of for the low frequency Whites line last time I checked, but it's been a few years since I moved on. I wish Detech would make a 12x10 DD for the low frequency Whites to breath new life into them in both depth and left/right separation along with handling mineralized ground better. Seems the perfect market because I bet there are more low freq. Whites coil compatible models on the market than any other machine...6000, QXT, QII, XLT, etc...Some of the best machines ever made, and a good larger DD coil than the 9.5" stock concentric I think would do wonders, as low freq. penetrates my soil better than higher ones in single frequency machines for me.
Far as a tiny coil, I had the 5.3" Bullseye or whatever for my QXT. Problem is it's really like 7" big or close to that, so it wasn't as small as I hoped. There is a smaller little coil that I think is around 4" but it's very rare to find. That's the one I'd look for if I wanted a trash coil, but unfortunately it too is a concentric.