This paper presents a very efficient optimization method suitable for multilevel combinational circuits. The optimization is based on incremental restructuring of a circuit through a sequence of additions and removals of redundant wires. Our algorithm applies the techniques of Automatic Test Pattern Generation (ATPG), which can efficiently detect redundancies. During the ATPG process, certain nodes in the circuit must have particular logic assignments for a test to exist. Based on the properties of these mandatory assignments, we have developed theorems to eliminate unnecessary wire redundancy checking. This results in significant performance improvement. The fast run time and the excellent scaling to large circuits make our Boolean optimization method practical for industrial applications.