Top panel: distribution of r/R-band rise times for SNe IIP, IIL, IIb, and SN 1987A-like SNe from the literature (Gall et al. 2015; Taddia et al. 2015a) and from this work. (See Filippenko 1997, for a review of SN classification.) We define as long-rising SNe II or SN 1987A-like events those with rise time >40 d. These SNe are powered mainly by radioactive decay at peak, whereas normal SN II peaks are dominated by shock energy. Bottom panel: r/R-band light curves of slow-rising SNe II (from this work, when colored, and from the literature), aligned to the peak epoch and scaled to match their peaks. All of them show rise times >40 d, but display a variety of shapes before peak. We also show SN 2005dp (Arcavi et al. 2012) and LSQ13cuw (Gall et al. 2015), which have relatively long rise times compared to normal SNe IIP, but still <40 d.