  We consider Deep Inelastic Scattering (DIS) thought experiments in unitary
Conformal Field Theories (CFTs). We explore the implications of the standard
dispersion relations for the OPE data. We derive positivity constraints on the
OPE coefficients of minimal-twist operators of even spin s \geq 2. In the case
of s=2, when the leading-twist operator is the stress tensor, we reproduce the
Hofman-Maldacena bounds. For s>2 the bounds are new.
