The paper copes with the problem of mixed-phase room response (RR) equalization. A minimum-phase multiple position RR equalizer recently proposed in the literature for room amplitude equalization is combined with a FIR group delay equalizer. The group-delay equalizer is designed in the frequency domain with a simple and computationally efficient but also effective and robust technique. Experiments performed on impulse responses acquired in different real environments have shown that the proposed equalizer is capable of improving the Clarity index in listening positions without introducing artifacts. Preliminary subjective tests have confirmed the improvement in the perceived audio quality.