Technical Abstract: Numerous investigators have concluded that improvements in weed management strategies that are minimally reliant on herbicides require the integration of multiple weed suppression tactics. However, the most cost-effective and efficacious ways to choose and combine tactics remain unclear. Here we suggest that the selection, deployment, and assessment of weed suppression tactics for organic and low-external-input (LEI) systems would be aided by supplementing empirical studies with models of weed population dynamics. Such models are particularly valuable for evaluating the likely impacts of various sets of tactics on weed populations five to ten years into the future. Our models predict the following for organic and LEI systems: (1) Reduced weed seedling recruitment, effected through the use of mulches and allelopathic cover crops, and reduced weed fecundity, achieved through the use of crop cultivars, densities, and spatial arrangements that increase crop competitive ability, should reduce weed population growth rates and costs of weed control. (2) Controlling weed seed production in the stubble of a harvested crop through timely mowing, selective herbicide application, or surface tillage should have strong positive effects on weed control in subsequent crops. (3) Weed seed predation should play a critical role in suppressing weed population growth, especially when tillage is delayed to retain weed seeds on the soil surface, and a diversity of crops is grown to provide continuous cover for seed predators. (4) Increased investment for several years in weed suppression through cultivation and hand weeding should result in lower cumulative weed control costs over the longer term.