Answer: There are broadleafed weed killers that spare grasses, and grass killers that spare broadleaf plants. There are also herbicides that kill all vegetation. There have been dozens of articles written about the pros and cons of each. But the bottom line is that you'll need to employ several strategies all at once to keep grassy weeds out of your broadleaf groundcover. Begin by removing all visible weeds, then applying a pre-emergent with a corn gluten base. Corn gluten produces an enzyme that inhibits seed germination, and can be used as a preemergent herbicide. If the weeds in your groundcovers are coming up from seed, then corn gluten is for you! You can get it from Gardener's Supply Co. (www.gardeners.com; ph# 800/863-1700); they call it WeedzStop. If the weeds you're dealing with are perennials that spread from runners or stolons, then you'll need to pull them out and mulch heavily under the ground cover, or clip them off to keep them under control.
Once your groundcover thickens up and shades the soil, weeds shouldn't be so much of a problem.
Good luck in your battle with the weeds!
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