ABSTRACT We use the low-redshift Zurich Environmental Study (ZENS) catalog to study the dependence of the quenched satellite fraction at 10 10.0 M ⊙ → 10 11.5 M ⊙ ?> , and of the morphological mix of these quenched satellites, on three different environmental parameters: group halo mass, halo-centric distance, and large-scale structure (LSS) overdensity. Within the two mass bins into which we divide our galaxy sample, the fraction of quenched satellites is more or less independent of halo mass and the surrounding LSS overdensity, but it increases toward the centers of the halos, as found in previous studies. The morphological mix of these quenched satellites is, however, constant with radial position in the halo, indicating that the well-known morphology–density relation results from the increasing fraction of quenched galaxies toward the centers of halos. If the radial variation in the quenched fraction reflects the action of two quenching processes, one related to mass and the other to environment, then the constancy with radius of the morphological outcome suggests that both have the same effect on the morphologies of the galaxies. Alternatively, mass and environment quenching may be two reflections of a single physical mechanism. The quenched satellites have larger bulge-to-total ratios (B/T) and smaller half-light radii than the star-forming satellites. The bulges in quenched satellites have very similar luminosities and surface brightness profiles, and any mass growth of the bulges associated with quenching cannot greatly change these quantities. The differences in the light-defined B/T and in the galaxy half-light radii are mostly due to differences in the disks, which have lower luminosities in the quenched galaxies. The difference in galaxy half-light radii between quenched and star-forming satellites is however larger than can be explained by uniformly fading the disks following quenching, and the quenched disks have smaller scale lengths than in star-forming satellites. This can be explained either by a differential fading of the disks with galaxy radius or the disks being generally smaller in the past, both of which would be expected in an inside-out disk growth scenario. The overall conclusion is that, at least at low redshifts, the structure of massive quenched satellites at these masses is produced by processes that operate before the quenching takes place. A comparison of our results with semianalytic models argues for a reduction in the efficiency of group halos in quenching their disk satellites and for mechanisms to increase the B/T of low-mass quenched satellites.