  We show explicitly that all partially and strictly massless fields with spins
s<=3 in (A)dS have null propagation. Assuming that this property holds also for
s>3, we derive the mass-cosmological constant tunings required to yield all
higher spin partially massless theories. As s increases, the unitarily allowed
region for massive spins is squeezed around \Lambda=0, so that an infinite
tower of massive particles forces vanishing \Lambda. We also speculate on the
relevance of this result to string theory and supergravity in (A)dS
backgrounds.
