This paper describes a theory that explains both the creativity and the efficiency of people's conceptual combination. In the constraint theory, conceptual combination is controlled by three constraints of diagnosticity, plausibility, and informativeness. The constraints derive from the pragmatics of communication as applied to compound phrases. The creativity of combination arises because the constraints can be satisfied in many different ways. The constraint theory yields an algorithmic model of the efficiency of combination. The C³ model admits the full creativity of combination and yet efficiently settles on the best interpretation for a given phrase. The constraint theory explains many empirical regularities in conceptual combination, and makes various empirically verified predictions. In computer simulations of compound phrase interpretation, the C³ model has produced results in general agreement with people's responses to the same phrases.