A system for correcting programming failures in an M-bit primary array of programmable fuses. The address of the failed fuse is stored in a secondary fuse array. Correction logic coupled to the primary and secondary arrays propagates the programming states of the good fuses, and corrects the programming state of the failed fuse, if any. The correction logic preferably comprises a decoder coupled to the secondary array which produces a one-hot M-bit word representing the failed fuse, and combinatorial logic arranged to receive the programming states of the primary array fuses and the one-hot M-bit word at respective inputs and to produce the correction logic output. Multiple failures can be accommodated using multiple secondary arrays, each storing the address of a respective failed fuse, or a tertiary array which stores the address of a failed fuse in either the primary or secondary arrays.