When installing new rear derailleur shifter cable I was suggested the following:
First set H limit screw (cable is not attached)
Move the derailleur by hand inward to adjust L limit screw
H screw controls outermost limit
L screw controls INNERMOST (towards the center of the hub) movement
Before attaching derailleur cable:
Screw in barrel adjuster ALL THE WAY IN
Then unscrew it 8 clicks
Then pinch the cable to the derailleur.
Adjustments:
The chain does not move towards inner cogs - too little tension, tighten the cable
The chain does not move towards quick release side cogs (outwards)- too much tension, loosen the cable
General principle:
More tension moves the derailleur towards the center of the hub (inwards)