Recent work by the author has extended the Supervisory Control Theory to include the class of control languages defined by pushdown machines. A pushdown machine is a finite state machine extended by an infinite stack memory. In this paper, we define a specific type of deterministic pushdown machine that is particularly useful as a discrete event controller. Checking controllability of pushdown machines requires computing the complement of the controller machine. We show that Exception Handling Controllers have the property that algorithms for taking their complements and determining their prefix closures are nearly identical to the algorithms available for finite state machines. Further, they exhibit an important property that makes checking for controllability extremely simple. Hence, they maintain the simplicity of the finite state machine, while providing the extra power associated with a pushdown stack memory. We provide an example of a useful control specification that cannot be implemented using a finite state machine, but can be implemented using an Exception Handling Controller.