U.S. agricultural producers are increasingly able to participate in private voluntary carbon initiatives that compensate their efforts to sequester CO2, reduce GHG emissions, and provide ecosystem services through eligible conservation practices. This study examines the potential effects of alternative private payment regimes (per practice vs. per output), prices paid to farmers relative to out-of-pocket costs (low vs. high), and the availability of information on CO2 sequestration (limited vs. full), on the adoption of cover crops and no-till in the United States, the resulting CO2 sequestration, and changes in farmers’ net returns. The analysis relies on a highly stylized model of heterogeneous farms calibrated with county-level agronomic data, and simulated for current estimates of GHG impacts of cover crop planting and no-till under different scenarios. Our results indicate that agricultural carbon markets can be profitable for U.S. farmers, although with substantial geographic variability, and that annual carbon sequestration could range between 17 and 75 million mtCO2e. Payments per output would incentivize higher carbon sequestration than payments per practice, but the former regime would be less favored by farmers as a unified group than the latter (due to lower aggregate net returns). However, if operators of farms with high carbon sequestration potential could decide the payment regime to be implemented, they would choose the payment per output regime (due to higher net returns per enrolled hectare). Total projected net changes in GHGs under payments per practice, based solely on county-average net GHG effects of cover crops and no-till, over-estimate actual total GHG sequestration (based on the entire distribution of net effects by county) by 2.1 and 14.2 million mtCO2e, or 18% and 21%, respectively.