Ive got weed issues also, most important is to keep them under control till the plants can compete with them. Next year Im going to put landscape fabric between my rows I think, it should help. I bought a big 4ft wide roll of heavy stuff online, gonna fold it in half and lay it between the rows, with rocks holding it down.
I've been laying fabric between the rows for years. It works. I used large nails and pins to hold it down this year. I never till between the rows. Not in the last 20 years.
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The flame article is good stuff. I need to find a smaller wand for my flower garden.