Add the salt, sugar, and butter to a pot or pan with a tight-fitting lid halfway filled with water.
Bring to a low boil over high heat, covered.
Clean the asparagus spears by snapping off the woody end where it bends naturally.
Peel away the remaining tough outer layer of each spear with a vegetable peeler, beginning about 1 1/2 inches from the tip of each spear.
Place the prepared asparagus in the pan, either lying down or standing up, in an asparagus basket that fits inside a tall asparagus or spaghetti cooker. Reduce the heat to medium and cover to keep the water at a simmer.
Cook for 8 to 10 minutes, or until a knife inserted into one of the stalks comes out smoothly.
Remove from pan and set aside to drain. Serve immediately with ham, melted butter, boiled new potatoes, and, if desired, Hollandaise sauce.