When a weed invasion is first discovered a decision has to be made on whether to attempt to eradicate it, contain it or do nothing. Ideally, these decisions should be based on a complete benefit-cost analysis, but this is often not possible. A partial analysis, combining knowledge of the rate of spread, seedbank longevity, costs of control and techniques of economic analysis, can assist in making a good decision. This paper presents a decision model to determine when immediate eradication of a weed should be attempted, or more generally whether weed control should be attempted at all. The technique is based on identifying two 'switching points': the invasion size at which it is no longer optimal to attempt eradication but where containment may be an option; and the invasion size at which it becomes optimal to apply no form of control at all. The model is applied to a woody perennial weed in a natural environment. The results show that seedbank longevity is the main constraint on the maximum eradicable area and spread rate is the main constraint on the maximum containment area. Stochastic simulations are undertaken to derive probability distributions of costs which are than used to evaluate the effect of budget constraints on areas that can be eradicated. We find that, in the absence of a budget constraint, it may be desirable to eradicate invasions from areas as large as 8000 ha, but when budget constraints typical of those faced by agencies in Australia are introduced, feasible eradicable areas are less than 1000 ha.