Hi, Yes, if you burn the garden you will damage any plants already coming up. Your best bet will be to get a sharp spade and dig up the weedy areas between your exisiting perennials. Of course, if you only have a few plants you want to rescue, then I might be tempted to dig them up, set them aside and then rake away all the dead weeds, do a light tilling and replant them. A lot of perennials are very forgiving if you move them in the very early spring when they are just breaking dormancy. Then, I would mulch heavily between the good plants to prevent weeds from coming back. Or, you can use a pre-emergent herbicide such as PREEN to prevent any weeds from sprouting. It should not hurt your plants. You just won't be able to start anything from seed in that area.