Danorocks method is great. Also, in the areas with warm tap water (mine is 85F in the summer), many of us use a "pre-chiller" -
easily built, its essentially a second immersion chiller - a coil of tubing placed in an ice chest filed with ice and water. It helps to drop a small pond pump in to keep the water circulating, and we're talking heavy on the ice, light on the water. You can even use rock salt to drop the temps a bit (like making ice cream).
Get your batch as cool as possible with your tap water, (assuming immersion or counterflow chiller) - then connect your pre-chiller such that the tap water gets cooled down even more before heading off to cool the wort.
In South Carolina summers, I can get my pitching temps to about 66F, then drop it into my fermentation chamber for the rest of the ride (62F).
Oh, and that 66F basement is great, but active fermentation can cause the temps inside the fermenter to rise as high as 10F, so it's possible you're hitting 74-76F during the most active days...