  We show that the external Compton (EC) model for the production of the GeV
emission in blazars makes specific predictions for the spectrum and variability
of those blazars characterized by a high Compton dominance (Compton to
synchrotron luminosity ratio). These unavoidable features have not been
observed, casting doubt on the validity of this popular model. We argue that
synchrotron-self Compton (SSC) models including the higher orders of Compton
scattering are more promising, and we briefly discuss the implications of our
findings for the geometry of the broad line region (BLR).
