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For a minimax finite impulse response filter, the group-delay error near the bandedges of the filter is usually much larger than the error elsewhere. A sigmoid function was recently introduced as a phase-error upper-bound function to effectively reduce the group-delay error near the bandedge. However, the manual selection of the function's parameters limits its flexible use in the design. This letter presents an iterative procedure to update the phase-error upper-bound function using a modified envelope of the absolute group-delay error, such that the resulting filter has near-uniform group-delay error, and thus to reduce the maximum group-delay error. Design examples demonstrate the effectiveness of the proposed iterative procedure.