We examine the curvature expansion of the field equations of a four-dimensi
onal higher-spin gauge theory extension of anti-de Sitter gravity, The theo
ry contains massless particles of spin 0, 2, 4, ... that arise in the symme
tric product of two spin-0 singletons. We cast the curvature expansion into
manifestly covariant form and elucidate the structure of the equations and
observe a significant simplification.