Removing surface roots without harming tree?

I have a couple pine trees in my yard, both are about 40 feet tall. Not sure exactly what kind they are, but one is pretty much a normal looking, straight up, short needle fir tree. And the other one branches off alot, looking somewhat like a cactus, and has needles roughly 2.5 inches long.

They both have a few surface roots popping up in the lawn that I'd be interested in getting rid of. Now I did a bit of research on the web, and almost every page I stumbled upon was highly against it, saying it could kill or severely harm the tree, or make it fall in a windstorm. It kinda scared me a bit, however none of those sites really mentioned any of the factors as far as how many roots are removed, how big, how far from the tree, or in what length of time.

So I'm wondering, is there a safe way to remove a couple roots without harming the tree? For example, I've spotted one surface root on each tree that I'd consider as one I'd like to see go. Each one is about 1.5 to 2 inches in diameter. One I'd like to cut back about 10 feet from the one tree, the other one I'd like to cut about 5 feet from the other. Would cutting such a small root off each tree really stand a chance of harming it? Aren't there hundreds of other roots, that each tree won't miss one small root?

Couldn't I cut those couple small ones (one from each tree), and wait a couple years before thinking about doing any more so the tree can recover? Or would those little 2" roots still have a drastic effect?