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Instantaneous priority multiplexing (IPM) is a recently proposed method for transmitting a number of black-and-white pictures through a channel that would otherwise suffice for only one black-and-white picture transmission, given that a certain amount of degradation is acceptable. To analyze this system, a mathematical description has been complemented by a simulation for the human observer in order to determine its performance properties. After careful consideration it has been found that the limit between acceptable and doubtful picture quality is identical with the theoretical limit for error-free transmission using an appropriate coding delay. The bandwidth compression factor for IPM transmission varies between 6 for line drawings and 1.5 for very black sketches. For the latter, "cross-vision" effects may become significant. As a successful approach to guarantee the required privacy in communication systems, a simple polyomino filter has been conceived which performs a certain feature recognition and pattern reconstruction. Owing to its simplicity, bandwidth saving by this improved version of IPM is an attractive alternative to the existing efficient encoding schemes for the multiplex transmission and storage of black-and-white pictures.