 This is a revised paper about the projections from retina to SC to two SC targets: the pulvinar and the parabigeminal nucleus. The paper uses an impressive array of circuit tracing and electrophysiological approaches to show that the retinal ganglion cells that provide (via the SC) input to these two target areas differ considerably. The paper has improved considerably in revision, and the central message is very clear and well supported by the data (with one important exception -- see below). The authors should be congratulated on both the work and on the strength of the revisions. I have a few suggestions below for clarity.  Subsection "Some visual responses of pulvinar and parabigeminal nucleus are explained by selective innervation of retinal ganglion cell types" (and later in the Discussion section): I don\'t think the lack of responses to full-field stimuli requires a nonlinearity. For example, you could have a linear summation of responses with oppositely signed weights from two sets of cells with similar responses to the chirp (or other full field) stimuli. I believe that in the LGN work the ganglion cells were combined with mostly or exclusively positive signs, so I think the difference here is that you either need a nonlinearity or a combination of responses with differing signs so that you can get cancelation.  