New oils with less ZDDP.
I have also read that diesel oils tend to still have more zinc in them. But the only way to know exactly which has what is to dig up spec sheets on them.
I've used 30w and 40w conventional racing oils for break-in, then go to Amsoil 0w-30 synthetic. I may go to conventional diesel oils when I run out of my racing oil stock and confirm which have the highest zinc content. I believe Valvoline has an oil listed for off-road use only because it's still a "racing" oil with zinc. I recall seeing several Amoil oils having a lot of zinc, including the diesel oils. It may have been on MSDS sheets but I can't find the spec sheets at the moment.
Amsoil source and info:
http://www.thelubepage.com