When calls offered to a primary group of trunks find all of them busy, provisions are often made for these calls to overflow to other groups of trunks. Such traffic overflow systems have been of interest for a long time, but recently overflow systems that allow for some calls to be queued have been of importance. In this paper we analyze a traffic overflow system with queuing, which consists of a primary and a secondary group. The system which we consider here differs from the two systems we investigated earlier, in that no overflow from the primary to the secondary is permitted if there is a waiting space available in the primary queue. As with the earlier investigations, we adopt an analytical approach which considerably reduces the dimensions of the problem, and simplifies the calculation of various steady-state quantities of interest. Our results include expressions for the loss probabilities, the average waiting times in the queues, and the average number of demands in service in each group.