Most oils still contain some ZDDP. Just being on the label is no indication that it is a good oil to use. What you need to know is the concentration. It needs to be no less than 1200ppm and 1300-1400 is best. The only oils that I know for sure are OK are Royal Purple and any of Amsoil's synthetics. Redline was OK as of late 2005 but I have not seen any new info. It is probably still OK. Valvoline VR1 is good too.
How much it has been reduced probably varies widely from one to another with some containing none at all. Just make sure the oil you use has at least the minimum.