  We investigate the structure of conformal Regge trajectories for the
maximally supersymmetric (2,0) theories in six dimensions. The different
conformal multiplets in a single superconformal multiplet must all have
similarly-shaped Regge trajectories. We show that these super-descendant
trajectories interact in interesting ways, leading to new constraints on their
shape. For the four-point function of the stress tensor multiplet supersymmetry
also softens the Regge behavior in some channels, and consequently we observe
that 'analyticity in spin' holds for all spins greater than -3. All the
physical operators in this correlator therefore lie on Regge trajectories and
we describe an iterative scheme where the Lorentzian inversion formula can be
used to bootstrap the four-point function. Some numerical experiments yield
promising results, with OPE data approaching the numerical bootstrap results
for all theories with rank greater than one.
