It is observed that ari algorithm proposed in 1985 by Kautsky, Nichols, and Van Dooren (KNV) amounts to maximizing, at each iteration, the determinant of the candidate closed-loop eigenvector matrix X with respect to one of its columns (with unit-length constraint), subject to the constraint that it remain an achievable closed-loop eigenvector matrix. This interpretation is used to prove convergence of the KNV algorithm. It is then shown that a more efficient algorithm is obtained if det (X) is concurrently maximized with respect to two columns of X, and such a scheme is easily extended to the case where the eigenvalues to be assigned include complex conjugate pairs, Variations exploiting the availability of multiple processors are suggested, Convergence properties of the proposed algorithms are established, Their superiority is demonstrated numerically.