We study the relationship between the two-agent implementation problem and the concept of interim efficiency of Holmström and Myerson (1983) in Bayesian environments with private values and independent types. We present a general property, called closure under interim utility equivalence,
and show it is sufficient for the implementation of social choice
functions. This condition, when combined with another property, called interim inseparability,
is also sufficient for the implementation of essentially single-valued
social choice sets. The characterization results are then examined in a
variety of environments.