A stereo plug has three connections on the inside -- one for a positive to the right channel, one for a positive to the left channel, and then a universal ground/negative. If you look at a regular stereo plug, the black bands separate your connections, so the tip is one positive connection, the middle section is another, and then the rest is the ground. I'll post a photo of the plug I wired up for reference.
Your stock Grado wire has four conductors -- a positive and negative for each channel, respectively, which separate at the Y, but both grounds are soldered to the same contact point in the 1/8" plug.
Edit:

That's the guts of your standard 1/8" plug. The tab on the left, where the red wire is soldered, is connected to the tip of the plug, while the right tab, soldered to the white wire, connects to the middle section. For my particular headphones, the red wire is the positive for the left channel and the white wire is the positive for the right. Below those are two navy blue wires I twisted together and then soldered to the long metal tab that hooks around the rubber sheathing, which is for the ground.
Edited by dirkgently - 12/18/11 at 3:44pm