if you don't want to slide around corners then get good quality tires, lower quality (in my exprince off brand/discount brand) tend to be harder rubber, and altho that can help slightly with mileage, it does not help with grip at all, an example of this was some RoadRunner tires (cheap brand) that my brother had, and every corner they squiled and sounded like you were doing a burn out or something, after a while the sound drove him crazy, along with the lack of traction so he switched to a better brand and it all improved.
I used to have 175mm wide tires, I currently run 165mm wide on my civic, and I've been knowen to corner fast insted of braking, traction has never been an issue, and like with snow tires, the tire store recomends narrower tires for better traction, and having gone from 175mm wide snow tires, to 155mm, I must say that the 155's feel very safe.
My scenario. I have two ford focus sedans. Identical bodywork/spoilers etc. Same engine / trans combo. One happens to be a 2000 and the other a 2004 but they are both well worn-in. The only difference is tires. one has 195 60-15, the other 205 50-16. The tire heights are fairly similar but the narrow tire car gets just under 10% better mileage on the highway. This has happened on more than one occasion where both cars went on a road trip, with one following the other, and the narrow tire car always took on less fuel. (I have not swapped tires from car to car to verify but I will test that this summer when the opportunity arises).