What oil has zinc now?

So then if synthetic isn't recommended for break-in, what would be the best choice? Good-quality conventional oil + break-in additive? And then just use Amsoil or another synthetic with good ZDDP levels after a couple thousand miles?
If you have the money for composite lifters you don't have to worry about break-in.

http://www.4secondsflat.com/Composite%20lifters.htm