Remember those black lumps from your camping grill? Activated charcoal (not the barbecue kind—buy food-grade stuff) is a superstar. It acts like a microscopic sponge. Fill a cloth bag or an old clean sock with it, drop it into your water pitcher, and let it sit overnight. The charcoal adsorbs nitrates and other muck.
You can find activated charcoal at pet stores (for aquarium filters) or health food shops. It’s cheap, reusable (just rinse and sun-dry it), and it feels a little like a magic trick. Your water might taste cleaner, and you’ll feel like a wise old alchemist.