If your cassette was like the one that came on my 2008 Specialized Globe, it was-
11-13-15-18-21-24-28-32
I absolutely hated it. I didn't need the 2 largest cogs and the 3T jump from 18 to 15 would almost blow my knee out.

I've since gone to a 12-23 9 speed with a 22-32-36 crank. (Emphysema prevents me from being able to use any higher gears)
Before going to the 9 speed I made up an 8 speed with some spare cogs I had laying around.
12-13-14-15-16-17-19-21.

IF you very seldom use the 11T cog, I'd suggest an 12-23 cassette. You could try your 34-24 combination to see if that seems suitable. Also if 24-24 will get you up all your hills, the 23T is only a bit higher.
12-13-14-15-17-19-21-23.