The dominance concept has proved of great value in multivariable design; essentially providing a condition which allows design on a single-input single-output basis. It also plays a key role in construction and analysis of iterative procedures for solving sets of linear equations. Three practical steps for achieving dominant transfer function matrices are discussed together with three classes of algorithms capable of solving relatively large problems and yielding solutions which are ‘optimal’ in a natural sense. The algorithms discussed solve:(i) optimum permutation of plant input-output relationships(ii) optimal scaling of plant variables(iii) construction of ‘real’ precompensation