I'm really dumb here -- can I add bleach (just household bleach?) to the pool even though I have a salt-chlorinator? Up until now all I do is add salt when it tells me to, and lo and slo (because the Ph is always that way with the salt-chlorinator and a new pool).

I've got some green algea growing in the spa (but not the pool although it's the same water system) and the water's crystal clear but this is the first time it's happened (and yes, on topic, this was right after it rained for the first time in a while here in Florida).