What's a better word for sole in this expression?
Solution 1:
One might say "instead of just increasing X," This means that only X will be increased to give the result. You could also say "compared to just increasing X," with the same meaning.
Solution 2:
"Compared to an independent increase in x" allows you to keep the sentence order and means only x increased. The problem is that this also says the increase in x did not depend on another factor. If you want to replace 'sole' but don't want to make a comment about it depending on something, you can replace independent with "exclusive."