A notification represents the proactive delivery of information to a user and reduces the need to visually scan or repeatedly check an external information source. At the same time, notifications often interrupt user tasks at inopportune moments, decreasing productivity and increasing frustration. Controlled studies have shown that linking notification delivery to the perceptual structure of a user’s tasks can reduce these interruption costs. However, in these studies, the scheduling was always performed manually, and it was not clear whether it would be possible for a system to mimic similar techniques. This article contributes the design and implementation of a novel system called Oasis that aligns notification scheduling with the perceptual structure of user tasks. We describe the architecture of the system, how it detects task structure on the fly without explicit knowledge of the task itself, and how it layers flexible notification scheduling policies on top of this detection mechanism. The system also includes an offline tool for creating customized statistical models for detecting task structure. The value of our system is that it intelligently schedules notifications, enabling the reductions in interruption costs shown within prior controlled studies to now be realized by users in everyday desktop computing tasks. It also provides a test bed for experimenting with how notification management policies and other system functionalities can be linked to task structure.