Do not remove more than one third from the asparagus. If neccessary, just cut off about 1-2 cm from the base and peel the lower third.
Additionally, it is not mandatory to peel the whole asparagus spears. In fact, most of the healthy nutrients are densely packed just below the skin and you probably don’t want to get rid of these.
Another tip: To avoid throwing away too much of this healthy food, use the cut or broken off ends for a fond/broth or soup.