Uneven basement floor -- need filler

I had sump pumps installed in my basement. The sump pump folks jackhammered up a perimeter around the family room of about 2.5 feet. They put concrete on it and tried to level it wth the rest of the concrete floor, which is under 1960s vinyl tile, and so there was a 1/8" drop between the old vinyl tile and the new concrete perimeter. I would like to lay new flooring over the tile -- haven't decided yet on laminate or carpet. I thought you might be able to feel the drop under carpet, and it might mess up the click-loc system on laminate. So after some thinking, I decided to fill in that perimeter with cheap self-adhesive vinyl tile first.
It almost works. The thickness is just right -- its 1/8" inch, and where it works there is no longer any drop or unvenness in the transition from the original vinyl tile. But the sump pump folks did not lay the new concrete perfectly evenly. A few of these new vinyl tiles "crunch" when you walk on them, as they are seesawing between high spots and low spots. My guess is that if I go ahead with the carpet or the laminate on top I would have crunchy parts of the floor. ("Crunchy parts" is a technical term.)
What can I put under the self-adhesive vinyl tile that would fill in some of this gap and make it lay -- if not perfectly flat, then flat enough? Preferably something with some give, perhaps something latex based?
Thanks!
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floor leveling compound, remove questionable tiles first. ideally you would use the floor leveling compound over the entire area
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Inquiringmind wrote:

out. If you use carpet it may be fine and not too noticeable. Could even fill really low spots with a bit of low pad or foam like goes under laminate flooring. its near the wall and not an area that usually gets walked on so I wouldn't spend too much time making it perfect for carpet.
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Thanks! After thinking about leveling, decided to go with carpet -- Milliken Tesserae Spectrum carpet squares, to be exact. I dont' think you'll be able to feel anything through them.
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