We apply a method for retrieving accurate moment tensors in the acoustic emission (AE) experiments based on the joint inversion of a family of AE events for their moment tensors and for the sensor amplifications including coupling effects between sensors and a specimen. The accuracy and efficiency of the method is tested on AEs recorded during three different temporal stages of a triaxial compression experiment on a cylindrical Bentheim sandstone specimen. The results show improved quality of the moment tensors indicated by significantly lower root-mean-square residuals between observed and predicted amplitudes. The approach is particularly suitable for detailed studies of the source parameters of AE events, to obtain accurate focal mechanisms and seismic moment tensors and for detecting fracturing regime of microcracks.