Photoshop :: Changing Photo To Just Four Colours,and Seperating

I need to change a photo into just four colours in preperation for producing a litho, this will allow me to have an image for each seperate colour, that when each colour is printed on the same paper, it makes up the final image, a bit like screen printing.

If you try the 'cutout' filter on a picture and adjust the amount of levels to 4, you will see the sort of thing I am trying to produce.

What I intend to do is once the image is seperated, create 3 other copies, then delete all unwanted colour sections, minus the colour I need for this particular part of the picture.

I have tried by converting the image to "indexed colour" and selected black and white, then entering 4 colours here.

This does give me 4 colours, however when I try to just select one of the colours and remove it, it looks like there is an underlying colour, i.e this colour selected is actually made up from two of the colours, as if it is mixed.