For just the reason you describe we do NOT recommend most algaecides, ever. The ONLY one we suggest using is Polyquat 60%. Its ONLY active ingredient should be "Poly...<something long and unpronounceable>...60%". It make be called Black Algaecide, Mustard Algae control, whatever. Only the ingredient matters. It does not foam but it can inhibit algae growth.

We also STRONGLY discourage using things like the HTH Super you describe. You want to use Tri-chlor with a 99% purity. Tri-chlor by its nature is highly acidic and adds stabilizer (CYA), which, if you need it, is good. If you don't, it's bad. But with "zinc and algaecide" is VERY, VERY BAD! I believe HTH knows it but doesn't care and sells it anyway because it LOOKS important and will get you to buy it. That's my opinion.

We think "cocktail" chemicals from pool companies only get you in trouble and empty your wallet.

Our FIRST and last recommendation for chlorine is....bleach. In certain situations we will recommend Cal-Hypo, Di-chlor powder, or tri-chlor tablets. But generally, bleach or its stronger sibling, liquid chlorine are best.