Put the bike in a stand, and shift to the smallest cog (your 12 or 11).
Look at the allignment of the derailleur at this position. The guide wheels/pulleys on the swing arm of the derailleur should be directly underneath the cog you are in. If not, your upper limit screw needs adjustment.
Should look like this rough diagram (one directly below the other, no angles):
H} <-- Chain on cog
H <-- Chain between cassette and derailleur
H] <-- Chain on upper wheel of derailleur
H] <-- Chain on lower wheel of derailleur
The lower limit should also be set so the chain/derailleur is in allignment in your largest cog (23,25,27... 28
).
Now, go back to 53x(11,12), and set your barrel adjuster on the derailleur to neutral ("centered" between fully in and fully out.) Shift to the next largest cog, and manually set your cable tension. Take out slack in the cable , and tighten the bolt which clamps the cable into the derailleur. If you do this manually, there should enough residual slack that you can't tighten with your hand to allow for shifting up into your 53x11 again.
Ok, back to 53x11 once more. Shift down one gear, and pay attention to how smoothly the gear is changing. If it is hesitant, rotate the barrel adjuster counter clockwise (looking from the rear of the bike) 1/4 turn.
Shift down again to your next largest cog on the cassette, and then repeat the barrel adjustment above if needed. Do this for each gear as you go from your high (11 or 12) to low (23,25,27) gears. Just adjust the tension with the barrel as needed to acheive a perfect shift.
If this doesn't work, I'd guess that your derailleur hanger is bent. Depending on the model and material it is made out of, you can either straighten it or buy a new one.
