Anyone plant mulberry trees? Any particular cultivars?

I love mulberrys. Second only to raspberries. The wild ones are fine but are there any that have been cultivated for better fruit production that have worked well for you?

I planted a variety about 5 years ago that was suppose to be "everbearing" or something like that. And it does set berries 2 or three times a year but they are too small to be worth picking (small kidney bean size). I'm thinking of cutting it down and planting a wild one in its place but first was going to see if there is anything better.