  A Quark-Nova (QN, the sudden transition from a neutron star into a quark
star) which occurs in the second common envelope (CE) phase of a massive binary
(Ouyed et al., 2015a&b), gives excellent fits to super-luminous, hydrogen-poor,
Supernovae (SLSNe) with double-peaked light curves including DES13S2cmm, SN
2006oz and LSQ14bdq (http://www.quarknova.ca/LCGallery.html). In our model, the
H envelope of the less massive companion is ejected during the first CE phase
while the QN occurs deep inside the second, He-rich, CE phase after the CE has
expanded in size to a radius of a few tens to a few thousands solar radii, this
yields the first peak in our model. The ensuing merging of the quark star with
the CO core leads to black hole formation and accretion explaining the second
long-lasting peak. We study a sample of 8 SLSNe Ic with double-humped
light-curves. Our model provides good fits to all of these with a universal
explosive energy of 2x10^52 erg (which is the kinetic energy of the QN ejecta)
for the first hump. The late-time emissions seen in iPTF13ehe and LSQ14bdq are
fit with a shock interaction between the outgoing He-rich (i.e second) CE and
the previously ejected H-rich (i.e first) CE.
