Bruce,
I do essentially what you describe, but add some balsamic vinegar to the asparagus after cooking.
As to the tough stems, my Mom taught me years ago that I should hold each stem of asparagus and move the bottom end towards the top. It will break off and a point that loses the woody stem. I check the asparagus in the store and if the stem bends rather than breaks, the asparagus is not fresh. Ideally the stem breaks about 1 to 2 inches from the bottom.
Ray