We present extensive optical and near-infrared photometric and spectroscopic observations of the stripped-envelope ( SE ) supernova SN 2010as . Spectroscopic peculiarities , such as initially weak helium features and low expansion velocities with a nearly flat evolution , place this object in the small family of events previously identified as transitional Type Ib/c supernovae ( SNe ) . There is ubiquitous evidence of hydrogen , albeit weak , in this family of SNe , indicating that they are in fact a peculiar kind of Type IIb SNe that we name “ flat-velocity Type IIb ” . The flat velocity evolution—which occurs at different levels between 6000 and 8000 km s ^ { -1 } for different SNe—suggests the presence of a dense shell in the ejecta . Despite the spectroscopic similarities , these objects show surprisingly diverse luminosities . We discuss the possible physical or geometrical unification picture for such diversity . Using archival HST images we associate SN 2010as with a massive cluster and derive a progenitor age of \approx 6 Myr , assuming a single star-formation burst , which is compatible with a Wolf-Rayet progenitor . Our hydrodynamical modelling , on the contrary , indicates the pre-explosion mass was relatively low , of \approx 4 M _ { \odot } . The seeming contradiction between an young age and low pre-SN mass may be solved by a massive interacting binary progenitor .