Try a reverse osmosis system. APEC (sold on Amazon and other places) has great reviews and makes counter-top screw-on types which take only a few minutes to ins

Try a reverse osmosis system. APEC (sold on Amazon and other places) has great reviews and makes counter-top screw-on types which take only a few minutes to install. It makes a huge difference in water quality. The under-the-sink models with a tank are nicer because it has a buffer for the filtered water, which gives you water faster until the buffer is depleted. The tankless ones take about 30 seconds to fill up a glass (based on water pressure). I use mine to fill up a 10 liter fusti once a week (takes ~an hour) which I keep in the fridge, since I live in an apartment with no option to install a real fridge with a water dispenser. It makes water taste so good that I prefer it over almost anything.