  We present a self-consistent way of modeling synchrotron self-Compton (SSC)
effects in gamma-ray burst afterglows, with and without approximated
Klein-Nishina suppressed scattering. We provide an analytic approximation of
our results, so that it can be incorporated into the afterglow modeling code
\texttt{boxfit}, which is currently based on pure synchrotron emission. We
discuss the changes in spectral shape and evolution due to SSC effects, and
comment on how these changes affect physical parameters derived from broadband
modeling. We show that SSC effects can have a profound impact on the shape of
the X-ray light curve using simulations including these effects. This leads to
data that cannot be simultaneously fit well in both the X-ray and radio bands
when considering synchrotron-only fits, and an inability to recover the correct
physical parameters, with some fitted parameters deviating orders of magnitude
from the simulated input parameters. This may have a significant impact on the
physical parameter distributions based on previous broadband modeling efforts.
