  We reconsider the issue of whether scalar-tensor theories can admit stable
wormhole configurations supported by a non-trivial radial profile for the
scalar field. Using a recently proposed effective theory for perturbations
around static, spherically symmetric backgrounds, we show that scalar-tensor
theories of "beyond Horndeski" type can have wormhole solutions that are free
of ghost and gradient instabilities. Such solutions are instead forbidden
within the more restrictive "Horndeski" class of theories.
