I have done both Bleach Only, TriChlor Pucks Only, and Pucks with Bleach for Shocking.

For my pool Trichlor Pucks with Bleach for shocking works best. Our pool has a low bather load (just my wife an I mostly) and I only use about 3 pucks per week. (22,000 Gal IG Vinyl).

I just turn the feeder flow rate to zero when shocking with bleach - and wait for the level to fall back where I want it and set it back to the normal flow rate.

Here is what happens when using all 3 of the methods.

Trichlor tabs are acidic, which will cause your pH to drift down. This will require that you add borax occasionally to adjust it. I check mine every day or two, and usually have to add borax once a week or so.

Bleach is basic, which will cause your pH to drift up as you add bleach. This will probably require that you add either dry acid (aka pH Minus) or Muratic Acid. When I used bleach last year I was adjusting my pH down about once every week and a half or so.

My preference is to handle the Trichlor pucks once a week, versus bleach bottles every 1 to 2 days. I also prefer adding borax to the skimmer to adjust the pH, versus having to deal with mixing Muratic Acid with a bucket of water before dumping in the pool. Muratic Acid is fowl smelling (before diluted) and nasty stuff.

If money were no object - I'd have a Salt Water Chlorine Generator, but I'm too cheap to put one in this year - but it may be on my spring shopping list for the 2007 season.