I love asparagus but it does have quite a distinctive, albeit delicate, taste and as Puddicat mentions, certain *ahem* tendencies...lol
I would not cook it for that long - just drop into boiling water (straight from the freezer) for about 3 minutes. I can only imagine that your spears were tough to start with, nought you can do about that... the thicker the spear, generally the softer they are. I put mine either in a quiche with a cream cheese and egg mix or serve them up simply boiled with butter and black pepper.
You could saut� chunks of the spears along with some onions and celery and then add some stock and cook until all the veg are soft.. Whizz through a blender or food processor to make a refreshing soup (I'd probably leave some of the veg chunks un-processed for extra texture).