Transient-based diagnosis of electromechanical failures in induction motors has gained an increasing attention over recent years. The diagnostic in some specific situations (presence of load toque oscillations, light loading conditions) or of specific failures may be difficult when using the classical MCSA approach. In this context, the transient-based methodologies have been proven to become valuable informational sources for the diagnosis, either confirming the MCSA results or avoiding its possible false positives. The application of these transient methodologies requires the use of modern signal processing tools that are in continuous evolution. This work proposes the application of an advanced tool; the recently developed Adaptive Slope Transform. The paper compares the performance of this continuous transform and that of a discrete counterpart, the Discrete Wavelet Transform, when applied to different controversial fault cases in which the classical MCSA may not lead to correct results: outer bar breakages in double cage motors and motors with rotor axial duct influence. The results show the potential of the continuous transforms for the transient tracking of high-order fault-related components as well as for the improved discrimination between fault components.