Companies tend to set their master production schedule weekly, even when producing and shipping on a daily basis—the term for this is staggered deliveries. This practice is common even when there is no marginal cost of setting a new schedule. This paper argues that the practice is sound for companies that use the ubiquitous order-up-to (OUT) policy to control production of products with a significant capacity cost. Under these conditions, the length of the order cycle (time between schedule updates) has a damping effect on production, while a unit (daily) order cycle can cause significant capacity costs. We call this the capacity cost trap. Developing an analytical model based on industrial evidence, we derive capacity and inventory costs under the staggered OUT policy, showing for this policy there is an optimal order cycle possibly greater than unity. To improve on this solution, we consider three approaches to smoothing: either levelling within the cycle, deferring excess production or idling to future cycles via a proportional OUT policy, or increasing the length of the cycle. By deriving exact cost expressions we compare these approaches, finding that smoothing by employing the proportional OUT policy is sufficient to avoid the capacity cost trap.