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A still open problem in the field of room response equalization is the development of perceptually useful mixed-phase equalizers. In a recent paper, a multipoint mixed-phase room response equalization system, integrating a minimum-phase multiple position room magnitude equalizer and a FIR group delay equalizer, was developed in the frequency domain. Starting from this approach, a mixed time-frequency algorithm is here proposed. The minimum-phase multiple position equalizer developed in the frequency domain, is combined with an all-pass FIR phase equalizer, designed in the time domain considering a suitable time-reversed version of a prototype function and taking advantage of the mixing time evaluation. Several tests have been performed considering real environments and comparing the proposed approach with the previous one, based on a group delay compensation. Subjective listening tests have also been done in a real environment, confirming the improvement in the perceived audio quality.