We assess current experimental constraints on the bi-doublet + singlet model
of top compositeness previously proposed in the literature. This model extends
the standard model's spectrum by adding a custodially-embedded vector-like
electroweak bi-doublet of quarks and a vector-like electroweak singlet quark.
While either of those states alone would produce a model in tension with
constraints from precision electroweak data, in combination they can produce a
viable model. We show that current precision electroweak data, in the wake of
the Higgs discovery, accommodate the model and we explore the impact of direct
collider searches for the partners of the top quark.