We characterized stratified deposits from the Upper Toluca Pumice at Toluca volcano, Mexico, to distinguish the various modes of transport at play in their genesis. Using the concept of hydraulic equivalence, we determined that deposits resulted from a combination of suspended-load fallout, saltation, and rolling. In particular, some well-sorted coarse stratified beds have a single pumice mode most likely indicative of clasts having traveled through both the transport system and the traction bed. Such beds are likely remnants of the sorting operated within the large-scale transport system. Other coarse beds have pumice and lithic modes suggesting rolling in the traction bed. We propose that boundary layer processes control the sorting of those beds and all finer beds. By helping to discriminate between transport mechanisms, hydraulic equivalences have a general applicability in geophysical flows involving clasts of contrasted densities.