Following the trends of index modulated (IM) techniques for optical communications, in the last few years several new waveform proposals have been made, aiming at conveying a higher density of information by driving different signal properties. One of these proposals mixes multi-pulse pulse-position modulation (MPPM) and quadrature amplitude modulation (QAM) in a system called QAM-MPPM. We present here a new way to demodulate its compound waveform, and, for the non-turbulent free space optical (FSO) channel, we provide accurate analytical expressions for its error probabilities, both in the case of the traditional and the new detector. Based on these analytical derivations, we also provide simplified expressions for the estimation of the error probabilities. We show that the new detector offers a gain of some tenths of dB in signal-to-noise ratio with respect to the previously defined one without an increase in complexity, and that our error probability estimations are more accurate than previously published results. To the best of our knowledge, this work is the first to provide simulation results validating the study of the error probability performance of QAM-MPPM.