Independent Vector Analysis (IVA) is an effective approach for Blind Source Separation (BSS) of convolutive mixtures of audio signals. As a practical realization of an IVA-based BSS algorithm, the so-called AuxIVA update rules based on the Majorize-Minimize (MM) principle have been proposed which allow for fast and computationally efficient optimization of the IVA cost function. For many real-time applications, however, update rules for IVA exhibiting even faster convergence are highly desirable. To this end, we investigate techniques which accelerate the convergence of the AuxIVA update rules without extra computational cost. The efficacy of the proposed methods is verified in experiments representing real-world acoustic scenarios.