Small-scale vegetable farmers are interested in cover crops and reduced tillage, but scale-appropriate technology and equipment are necessary to expand these practices to the growing segment of small farms. We sought to determine the efficacy of tarps, an increasingly popular tool on small farms, to end overwintering cover crops and provide weed suppression for subsequent no-till cabbage production. In three fields over two seasons in Maine, we grew a winter rye (Secale cereale L.) and hairy vetch (Vicia villosa L.) cover crop, which we managed by a factorial combination of tillage (no-till, till) and tarping (tarp, no-tarp) in June, followed by a transplanted cabbage crop (Brassica oleracea L. var. Capitata) in July. Within each treatment, subplots were either weeded by hand or left unweeded. Cover crop biomass ranged from 2.8 to 4.5 Mg⋅ha−1. Mean cabbage weights in the novel no-till system (no-till/tarp) were greater than (year 1) or equal to (year 2) those in tillage-based systems (till/no-tarp and till/tarp). In year 1, the mean cabbage weight in weeded subplots was 48% greater in no-till/tarp than in till/no-tarp systems. In unweeded subplots, this difference was 270%, highlighting the efficacy of the no-till/tarp system to reduce the impact of weeds. In year 2, weed biomass was higher with all treatments than it was in year 1, and unweeded subplots failed to produce marketable heads (i.e., >300 g). The mean cabbage weight in weeded subplots was equal among no-till/tarp, till/tarp, and till/no-tarp systems. Tarping had a strong effect on weed biomass and weed community composition measured at the time of cabbage harvest in unweeded subplots. In year 1, weed biomass at the time of cabbage harvest with tarp treatments was less than half that with no-tarp treatments. Tarps effectively facilitated the cover crop mulch-based no-till system. We propose that this system is an adaptive strategy for farmers affected by climate change. However, both cover crop production and tarping shorten the growing season. We discuss tradeoffs and opportunity costs using the metric of growing degree days.