Abstract: We present observations of four rapidly rising (t(sub rise) approximately equals 10 days) transients with peak luminosities between those of supernovae (SNe) and superluminous SNe (M(sub peak) approximately equals -20) – one discovered and followed by the PalomarTransient Factory (PTF) and three by the Supernova Legacy Survey. The light curves resemble those of SN 2011kl, recently shown to be associated with an ultra-long-duration gamma-ray burst (GRB), though no GRB was seen to accompany our…