Exotic species are a widely recognized environmental and economic problem; introductions are attributed to the movements of travelers and traded goods.  The US Department of Homeland Security annually inspects around half a million ships and airplanes and over 60 million people; almost 2 million interceptions of plant material, pests, meat and poultry products are made yearly, yet the percentage of travelers and cargo inspected is small.  Given such constraints, the need to efficiently target inspections is widely acknowledged.  In this paper we derive an optimal inspections regime with learning.  The model is applied empirically to a dataset on agricultural pest inspections.  When shipment inspection leads to an interception, the reward (averted damages) is readily inferred.  Before the goods are examined a simple expected value calculation justifies the prioritization of shipments deemed high risk.  Importantly, a second reward from inspections exists. Because the probability of infection of a shipment is uncertain, the outcome of each inspection can be used to learn and thus guide future inspections. While straightforward in concept, this value accrues diffusely over all future periods.  How does incorporating this second effect influence inspections? Specifically, what are the conditions under which the delayed value of learning (from inspecting the lower risk, higher uncertainty shipment) outweighs the immediate cost of elevated invasion risk?  Our Bayesian learning model addresses this question, and suggests, for example, that inspections should be more heavily focused on trade in new products or with new partners, even if their expected damage is low.