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An acid wash would NOT be the best thing. Acid washing works by CORRODING off the top layer of pool plaster. What's left is whiter, but also rougher, more porous, and MUCH more susceptible to algae and staining.

Rent a LOW POWER pressure washer (ideally, a low power high volume washer) and pressure wash your pool. GREAT way to get an all over tan, because the sun reflects off the sides onto every thing but the soles of your feet. Of course, if you don't tan, slather the sunscreen on!

Be careful: high pressure can cut the plaster as badly as acid, so don't over do it. It can also cause SERIOUS skin infections, so don't accidentally spray yourself.

Do NOT try to remove 100% of the stains -- let chlorine do that later. Instead, get the bulk of it and refill. It would help if you slosh a 5:1 water / bleach mix on the sides. Doing so will help remove the marks AND give you an algae free start up.

When you do it, do not wear any clothes or swimwear you like; do wear sun glasses or safety glasses; do wear cuffed gloves; do NOT leave the bleach mix on your skin for long periods. I'd do it in an old swimsuit, gloves, and flip flops, and keep a hose running gently near me to clean off splashes. A plastic bristle broom will help you spread the stuff around. If you've removed the goop first, you can leave the bleach mix in the pool on startup. Just make sure it's diluted some by pool fill before you start your pump.

PoolDoc