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Two algorithms for the design of two-dimensional optimal Chebyshev FIR digital filters have been proposed independently by Kamp and Thiran and Hersey and Mersereau. Both make use of an iterative ascent algorithm. A modification of the Hersey-Mersereau algorithm based on a suggestion made by Rice is briefly described here along with a review of the other two techniques. Results of an empirical comparison of convergence rates indicate that the original and modified Hersey-Mersereau algorithms converge more rapidly than the algorithm of Kamp and Thiran. The modified algorithm is shown to exhibit the most rapid convergence.