  We present a new, more nuanced understanding of non-linear effects in inverse
Compton sources. Contrary to what has been heretofore understood, deleterious
non-linear effects can arise even at low laser intensities, a regime previously
viewed as linear. After laying out a comprehensive survey of all non-linear
phenomena which degrade the effectiveness of inverse Compton sources, we
discuss two powerful techniques designed to remove these non-linearities.
Starting with the known technique of longitudinal chirping of the laser pulse,
which we developed earlier to mitigate adverse non-linear effects in the high
laser field regime, we have discovered that the simple stretching of the laser
pulse, while keeping the energy constant, can significantly increase the
spectral density of the scattered radiation in many operating regimes. Our
numerical simulations show that combining these two techniques removes
detrimental non-linearities and improves the performance of inverse Compton
sources over an order of magnitude.
