Streaming systems often use slices to share computation costs among overlapping windows. However they are limited to instantaneous events where only one point represents the event. Here, we extend streams to events that come with a duration, denoted as spanning events. After a short review of the new constraints ensued by event lifespan in a temporal sliding-window context, we propose a new structure for dealing with slices in such an environment, and prove that our technique is both correct and effective to deal with such spanning events.