[Closed] shifting problems...

Just got my first road bike in a few years and am working my way through rebuilding it. I'm struggling with the shifting, I think I know the problem but just wanted to get some other perspective.

I can adjust the cable tension to up shift without problem, however down shifting is poor.

OR

I can adjust the cable to down shift, again without problem, but up shifting is poor.

My first guess is a dragging cable, so I'll change that out, second guess is a stiff rear mech - I'll get it in a parts cleaner and re-lube it. Anything else to consider, could a chain, or worn rear cassette cause this too??