You're on the right track, but it's not quite that simple.
The cooling load is divided into (2), the sensible cooling load (heat) and the latent cooling load (humidity). Doubled insulation will decrease by half the sensible cooling load, but will have little effect on the latent. For that, you need to decrease the ACH (air changes per hour, or air leakage) and not go inside and out so much.
In fairly humid climates (the east, midwest, and south), the latent cooling load can be from 30-65%, so something has to be done about that, too, to decrease the total cooling load by 1/2.
There were some posts on earth tubes above. Care needs to be taken with them to make sure they drain the humidity in a sensible (no pun intended) way.
My ideal system is to have a house bermed on the north side on a south-facing slope (reverse that for south of the equator). Dig a trench 4-6' deep for 3 6-8" pipes (separated in the trench) buried along about 100', slightly (or more than slightly) uphill. 2 of the pipes will have a 180 degree elbow at the upper end, making a loop, the other one will have an inlet for outside air.
The outside air inlet pipe will cool fresh air pushed into the house without a fan, since the cool air will weigh enough to push it down the hill; however, you should restrict the use of this one, since it has to cool down air from outside, which is presumably hotter than the house air, and will eventually warm the trench if you use it all the time. The loop, once it gets primed with a fan should set itself up with a siphon since the air returning to the house is cooler than the air going up the hill, and will run without power (albeit not that fast).
The cool thing about both of these is that the hotter your house is (relative to the earth temperature), the faster the air will flow, and more heat transfer will take place. Also, because of the slope, it's trivial to collect the water and remove it since it will flow towards the house.
Now for the bad news: if you live in the deep South, the earth just isn't cool enough to make this work; also, you do need superinsulation in most parts of the US, otherwise the trench length, depth, and pipe size will be quite large to keep up with the cooling load.
A/C, SchmA/C, we don't need no stinkin' A/C !
Dave