Companion planting asparagus

We are prepping our asparagus beds for winter planting for the first time. This is in our kitchen garden which is fenced away from all our animals. We have roughly an 8'x10' section. What would you recomment planting with it? We are in Houston, TX, and it is an almost completely sunny spot. I definitely want something to grow there but am not sure what type of plant - maybe something like sunflowers that would shade the ferns a bit in the summer but be gone by spring when the asparagus is growing? And it wouldn't distubr the aspragus roots to plant?

Asparagus doesn't mind sun, and it's the mature plants that need it most, not the young sprouts.  I find the challenge with it is that it's kind of a space-hog by itself, so companion planting is a good idea...but how?  The big ferny plants are itchy to walk among and also sort of brittle....a summer asparagus patch isn't a pleasant place to be in.  Winter squash is one thing I've done....the vines grow under the ferns and you don't have to harvest till fall and only once.  You can plant this in holes here and there, even along the edges of the plot and train the vines to go in and under.  The other thing is the whole patch is empty in the winter....the ferns die and you can cut them, and the new sprouts don't show up till spring is well advanced....so it's a good place to grow winter stuff if your climate is amenable to it....but yes you would want to transplant into it or take out very shallow seed rows so as not to disturb the roots of the asparagus.  Right now, I'm "companion planting" my asparagus with geese!  The area has a bermuda grass problem, which isn't much of an issue for the asparagus itself, but it makes growing anything else with it pretty much impossible.  Except for geese!

Not much room for anything else. Asparagus has no known pests in texas. Only thing recommended is remove the growth when it dies. Something about the seeds attracting pests, but havent experienced this in texas.

The Direct Tv guy dug a hole in the middle of my patch to put the dish in. It was winter and i had removed all the tops. Not his fault.  

I have my zone 6 asparagus planted in a long row, with rhubarb on one side and strawberries on the other as ground cover. Basil is interplanted, with horseradish and ginger on either end of the row. An about 10 foot pollarded mulberry is off to one side with a grape trailing through it, giving it some protection during the hottest hours of the day.

I also have strawberries under my asparagus.  It just seemed like a good idea, and when I looked it up it seemed more than one person had also thought so.  I did have a grand plan to make a low cage for the strawberries with a weld mesh roof that the asparagus could go through and be supported by, but open sides that I could temporarily put on when the strawberries needed protection.  My major problem with the asparagus is slugs though, and the strawberries walked off elsewhere, and it didn't seem worth building a cage yet.