Answer: Threadleafed coreopsis can be trimmed off at the ground, being careful not to damage any tiny, newly emerging shoots. Virtually all of this plant will simply fall away into your hands by spring.
Lance leafed coreopsis can also be trimmed off very short to remove cold damaged stems and leaves. On this plant, however, you may find some still green foliage or some emerging growth at the crown. Be careful not to damage this as you trim away the brown parts.
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