Popper proposed that a putative set of laws be regarded as a scientific theory only if there exist possible empirical observations that would falsify it. \textit{H. A. Simon} and \textit{G. J. Groen} [ibid. 24, 367-380 (1973; Zbl 0291.02034)] proposed that Popper's test be formalized by conditions of finite and irrevocable testability (FITness). The present paper provides an amended formulation of the FITness criteria that removes several difficulties and ambiguities from the 1973 formulation. A theory, F(T,O) is finitely testable if there is at least one set of observations that is not completable to a model for the theory, and for every such set there exist finite subsets that are not completable to a model. A theory is irrevocably testable if, when disconfirmed by some set of observations, O, there is no superset of O that is completable to a model of the theory. Finite testability implies irrevocable testability, hence FITness. The theoretical terms are always Ramsey-eliminable from a FIT theory. Examples are provided of theories that are and are not FIT, and it is shown that certain ''pathological'' examples that have been discussed in the literature are not FIT.