I bought some pencil-thin asparagus which I planned to snap before steaming. After picking up the first 2 spears to find that the bases weren't hard enough to readily snap, I threw caution to the winds and just cut off the bottom eighth inch from the whole bunch, to remove anything that might be truly tough. After steaming, I was pleased to find that with the exception of 3 or 4 spears out of a couple of dozen, the entire spears were tender enough to eat. The finger-thick ones certainly need at least SOME trimming, if not peeling, but I'll no longer trim thinner stalks unless I am planning on making vegetable stock.
The first asparagus I ate were big fat and white in Germany. These are always snapped and peeled. Back in Canada when I served green asparagus the same way my relatives couldn't believe I went to the trouble because they never did this with fat or thin asparagus. I still peel unless they are just too thin.
If the asparagus you purchase were gotten from the Brooklyn Heights store in which I'm forced to find mine, you would have most likely had to trim off virtually the whole stem, up to about an inch from the top. That store doesn't seem to know that asparagus should be displayed in either a standing position or on its side--WITH COOL WATER UNDERNEATH. When left for a day or two in dry surroundings, it's practically dry enough to kneed into dust! But then, not all of today's food store employees are trained to know such elaborate info, right?