Perfectly removing a white background

This might help someone else.  I am also writing this so I remember it.  This procedure makes a flat photoshop document with all white removed as if the document were a layer with blend type "Multiply".  You can then paint white behind it to make non-translucent sections for overlaying with other things (in other programs or web stuff), but the edges will be perfect with no loss of detail.

1. Open the doc (RGB mode only)
2. Make a new layer, fill it with full red.  Invert it (Cmd-i).It'll go cyan.
3. Make a layer, fill it with green.  Invert it, so it goes magenta.
4. Make another layer, fill with blue, invert to make yellow.
5. Turn off the new layers so you can only see your original.
6. Go to the channels palette.
7. Create three new blank channels. They'll be black.
8. Command-click the Red channel.  This will make a selection.  Change to your first new channel, and fill that selection with white.
9. Do the same thing for the green channel, into your second new custom channel.
10. Do the same for the blue channel, into the third custom one.
11. Control click your first custom channel (with the selection from the red layer). Invert the selection (command-shift-i). Go to your new red layer (which is now cyan), and apply the selection as a mask (by clicking the mask button).
12. Do again using custom channel 2, onto the new Green (changed to Magenta) layer.
13. And again, from channel 3, into the Blue (now Yellow) layer.
14. Set all 3 of your layers to blend type "Multiply"
15. Turn off any other layers.

Done.  If you need to, make a new layer under, and paint white to make any sections you want opaque.