Vinyl and Linoleum Flooring - Laying vinyl tile on 2 different surfaces: which to remove?

Not sure if the thread title makes any sense. Here's a better description:

I want to redo my bathroom area with some Armstrong peel+stick vinyl tile. Currently, there is carpet over about 2/3 of the area, and vinyl sheet over the other 1/3. There is concrete under both. Obviously I need to remove the carpet, but I'm not sure what to do about the vinyl sheet. I suppose my choices are
1) raise the level of the concrete (formerly carpet) 1/8" to the level of the vinyl sheet, then put the tiles over the raised concrete and over the vinyl sheet
2) remove the vinyl sheet as well, so that the entire area is the concrete base, and install the tile over that

While it seems like it would be 'cleanest' to remove all the surfaces down to concrete, I am concerned about the difficulty in removing the vinyl sheet. Any opinions on whether I should just leave it and raise the level of the concrete? If I go that route, what's the easiest way to raise the concrete up to the vinyl sheet level? Self leveling concrete? That certainly sounds simple enough, but perhaps it's not easy to work with.

The total area is about 60sq.ft., with 40 of it currently carpet and the other 20 vinyl sheet.

Thanks!
Kevin

no doubt. remove the vinyl. its not hard at all. a large scraper and it will come right up = depending on how it was installed.

hey thanks for responding! Should I expect a lot of leftover glue residue from the vinyl? Also, there is a toilet in the vinyl area...anything special I need to be aware of in terms of removing it first? Thanks a ton.
-Kevin

well. like i said, it depends on how it was installed. mine was just glued around the parameter. about 6 to 10 inchs. if you are put vinyl back on, don't worry about the old glue. just make sure the concrete is smooth.

slc is kind of a pita to work with. and to put vinyl over it. i wouldn't even consider it.

removing a crapper. if you can't do this, don't do anything. its easy. just use common sense.

i all so would try to remove ext.vinyl. you will have glue, and depending on how good it is adhered felt backing still left on concrete. razer scraper will work just fine to get the felt up .Patch the floor [skim coat underlayment] to cover left over glue and to smooth conctere to prep area for install of new floor. plan b would be to use patch to ramp down 1/8"vinyl to concrete about 16" and go over with new flooring