After receiving a message that defines an initial target area for distribution of an alert, a wireless carrier network may identify a first set of one or more coverage areas that are fully encompassed within the initial target area and a second set of one or more coverage areas that are partially encompassed within the initial target area. For each partially-encompassed coverage area, the network may then define a respective target area that is less geometrically complex than the initial target area. In turn, the network may broadcast the alert (1) in each fully-encompassed coverage area in a manner that directs a recipient device to output the alert regardless of the device's location and (2) in each partially-encompassed coverage area in a manner that directs a recipient device to output the alert only if the device's location is encompassed within the respective target area for the coverage area.