The major difficulty encountered in the conduct of a comprehensive search for radio signals of extraterrestrial intelligent origin is the vast range of fundamental parameters that must be examined to make significant inroads on the plausible signal regime. This problem is aggravated by the almost certain occurrence of mistaken detections caused by stochastic processes and by man-made radio frequency emissions. Each such mistake, unless quickly and unambiguously characterized as a false alarm, will require repetitive observations during the conduct of the program. This wasted time will, in effect, reduce the sensitivity achievable in a given search duration. This paper examines the implications of false alarms on the search system design, performance, and application and, in particular, on the choice of the data-processing approach. We show that, by an approach that limits the requirement for repeated observations, the degradation caused by false detections can be constrained to less than approximately 40%, whereas, without this restriction, the degradation might be severe. By modeling the mistaken detections caused by man-made devices as a Poisson process, we can place an upper bound on the probability of false alarms as a function of the detection threshold and of the number of interferors in the hemisphere. The understanding developed by these considerations suggests an experiment protocol consisting of a set of sequentially applied criteria to limit the range of parameters that need to be considered in declaring a false alarm, thus decreasing the time required to make this declaration and enhancing the performance of the search.