The vast majority of Type II supernovae (SNe) are produced by red supergiants (RSGs), but SN 1987A revealed that blue supergiants (BSGs) can produce members of this class as well, albeit with some peculiar properties. This best studied event revolutionized our understanding of SNe, and linking it to the bulk of Type II events is essential. We present here optical photometry and spectroscopy gathered for SN 2000cb, which is clearly not a standard Type II SN and yet is not a SN 1987A analog. The light curve of SN 2000cb is reminiscent of that of SN 1987A in shape, with a slow rise to a late optical peak, but on substantially different time scales. Spectroscopically, SN 2000cb resembles a normal SN II but with ejecta velocities that far exceed those measured for SN 1987A or normal SNe II, above 18000 km/s for H-alpha at early times. The red colours, high velocities, late photometric peak, and our modeling of this object all point toward a scenario involving the high-energy explosion of a small-radius star, most likely a BSG, producing 0.1 solar masses of Ni-56. Adding a similar object to the sample, SN 2005ci, we derive a rate of about 2% of the core-collapse rate for this loosely defined class of BSG explosions.