Why did you change the cassette?

Were you trying to tightening the spacing between the gears?

Or, didn't need the 30T low gear?

Or, wanted the higher 11T gear?

If you just want to tighten the gear spacing, and don't need the 30T, and if the old cassette and the new cassette are from the same manufacturer, you can swap parts to make a cassette with custom ratios. On Shimano cassettes the two smallest cogs are loose, and easy to swap (after removing the lock ring). On some other brands of cassettes all the rings are loose, and you can swap any ring easily (you can also free the rings that are bolted or riveted together on Shimano cassettes).

For instance, let say you don't need the 11T top gear on the new cassette, but you want the 28T. You could take the 12T top gear (and the next gear 14T? if you want) from the old cassette and swap out the 11T (and 2nd gear 13T?) and make yourself a 12-28 cassette (using whichever 2nd cog fits your riding style better).

Kill two birds with one stone as it were. Top gear will be a little lower and easier to pedal, and you will eliminate your sagging chain in the small-small without shortening the chain or replacing the rear derailleur.