Winter cover crops/green manure

My cover crop seems to grow automatically, bittercress! Then again if you sow something all over and then dig it in, aren’t you digging in all the weeds that have come up along with the green manure. Each year I've got grass, bittercress, groundsel , dandelions, clover, etc coming up in the veg patch, I wouldn't want to dig all that in as well. Not that I'm going to bother with cover crops. PS how does No Dig cope with cover crops - basically what V was asking.