To improve the rate of convergence of the direct search optimization procedure using random numbers and search region contraction as introduced by LUUS AND JAAKOLA [1], called LJ optimization procedure, a multi-pass method is suggested, where the region size for each variable at the beginning of each pass after the first one is determined from the extent of the variation of the variable during the pass. Computational experience with several typical chemical engineering systems shows that such a procedure enables the optimum to be determined more efficiently than arbitrarily choosing the legion sizes through some preliminary runs, or by some intuitive approach. For illustration and evaluation of the approach, three examples are chosen. The first example involves an alkylation process consisting of ten variables and seven equality constraints. The second example involves model reduction, and the third example is a non-linear nonseparable optimization problem involving 300 variables. In each case, the method was found to be robust, and the optimum could be obtained considerably faster with this newly proposed method of region size: determination.