  The thermodynamic stability of large AdS$_3$ black holes implies that Cardy's
$\Delta\rightarrow\infty$ formula for the density of states remains
approximately valid when $\Delta\sim c$ in holographic 2d CFTs, constraining
their light spectra. Averaged OPE coefficients take a similarly universal
asymptotic form, and black hole arguments again imply an extended regime of
validity. In this note we study conditions under which the OPE asymptotics
extend to $\Delta\sim c$ at large central charge. Some of the conditions found
are stronger than required by an extended Cardy regime and are violated by
permutation orbifolds, such as the D1-D5 system at zero coupling. Our results
suggest new bounds on non-vacuum block contributions to correlation functions
in holographic CFTs.
