Moisture retention is an issue for our shallow-rooted crops in the summer, but definitely not an issue fall through spring. I do mulch in the summer when I have a good source of mulch, but I need to be careful. Last year I put grass clippings on, but too late. The grass had tons of new seeds in it and by late fall I had a nice lush crop of lawn grass on my beds. Oy! I had this happen once before with in ground crops that I mulched heavily with bedding straw. The straw was full of seed heads and created a real mess in pathways. I do use shredded leaves in fall but need to get more than our yard produces. Daikon radishes are great for a fall crop in in-ground beds. They set very deep roots. I don't think that would work for our raised bed, but maybe there is a shorter variety?@begreen , I'm surprised that moisture retention is a problem for you with such low annual rainfall. I guess it all comes at the wrong time of year for you or something. Do you use a mulch on your beds in the winter? Or cover crops?
Use BT and maybe diatomaceous earth for cabbage worms. Spinosad is harmful to bees.