  We present the light curves of the hydrogen-poor superluminous supernovae
(SLSNe-I) PTF12dam and iPTF13dcc, discovered by the (intermediate) Palomar
Transient Factory. Both show excess emission at early times and a slowly
declining light curve at late times. The early bump in PTF12dam is very similar
in duration (~10 days) and brightness relative to the main peak (2-3 mag
fainter) compared to those observed in other SLSNe-I. In contrast, the
long-duration (>30 days) early excess emission in iPTF13dcc, whose brightness
competes with that of the main peak, appears to be of a different nature. We
construct bolometric light curves for both targets, and fit a variety of
light-curve models to both the early bump and main peak in an attempt to
understand the nature of these explosions. Even though the slope of the
late-time light-curve decline in both SLSNe is suggestively close to that
expected from the radioactive decay of $^{56}$Ni and $^{56}$Co, the amount of
nickel required to power the full light curves is too large considering the
estimated ejecta mass. The magnetar model including an increasing escape
fraction provides a reasonable description of the PTF12dam observations.
However, neither the basic nor the double-peaked magnetar model is capable of
reproducing the iPTF13dcc light curve. A model combining a shock breakout in an
extended envelope with late-time magnetar energy injection provides a
reasonable fit to the iPTF13dcc observations. Finally, we find that the light
curves of both PTF12dam and iPTF13dcc can be adequately fit with the
circumstellar medium (CSM) interaction model.
