Most work on diagnosis of digital circuits has concentrated on the model of stuck-type faults. Although these faults are probably the most important class of faults, other types of faults do occur in practice and the occurrence of these other faults may affect the diagnosis of stuck-type faults. In this correspondence we consider the problems associated with detection of two other fault models, shorted diode and input Bridge faults, both corresponding to shorts. We present procedures for generating tests for stuck-type faults which also detect these other faults if they are detectable. Unlike stuck-type faults, the presence of undetectable short-circuit faults does not imply that the circuit can be simplified by removing inputs or gates. Undetectability of short-type faults corresponds to the ability to move fan-out points from an input to an output of a gate without changing the function realized by the circuit. Elimination of this type of redundancy does not necessarily lead to a simplified circuit.