A procedure for identifying functionally equivalent faults and improving the performance of diagnostic test pattern generation is described in this paper. The procedure is based on evaluation of faulty functions in cones of dominator gates of fault pairs. This is enhanced by utilizing circuit redundancy information. Equivalence is proved without the previously required circuit transformations. Stem-branch equivalences for reconvergent stems and their branches are identified efficiently obviating the need to check for non-masking and multiple-path sensitization. Both static and dynamic techniques are developed to exploit relations among inputs of dominator cones. This reduces the simulation time required by the procedure and enables evaluation of larger cones than could be evaluated earlier. As a result, more equivalent fault pairs are identified. Experiments performed on ISCAS85 circuits and full scan ISCAS89 circuits are used to demonstrate the effectiveness of the proposed techniques.