Steve, I'm not quite getting it. You say that you have a crop three years old, and you planted 20 crowns last year. Elaborate a little bit more. Did you plant the crowns at least 1 foot apart? Pardon me, I am not trying to be an expert, but I want to see if I can help you.
These crowns that you planted last year, don't touch them for at least another 2 years, allow them to mature to provide food for you.
The crowns that you have had in for three years, now this year they should begin to produce some that you can eat, don't take them all. Leave lots in the ground to grow up to produce next years crowns, which you should begin to harvest even more.
With asparagus you need to look at the big picture, years down the road. No harvesting until after the third year, and then only a few. The fourth year and forward they will provide food for the table.
Did you put lots of manure on compost on them? They are heavy feeders, really heavy. They love, and I mean love, to be fed, lots.......They like drainage, they like lots of moisture too at the same time.
So, friend, elaborate. I might be able to help you out a little bit, lean on me. Have a wonderful and beautiful day, love our lives we live. Cindi