Noun-noun compounds play a key role in the growth of language. In this article we present a system for producing and understanding noun-noun compounds (PUNC). PUNC is based on the Constraint theory of conceptual combination and the C-3 model. The new model incorporates the primary constraints of the Constraint theory in an integrated fashion, creating a cognitively plausible mechanism of interpreting noun-noun phrases. It also tries to overcome algorithmic limitations of the C-3 model in being more efficient in its computational complexity, and deal with a wider span of empirical phenomena, such as dimensions of word familiarity. We detail the model, including knowledge representation and interpretation production mechanisms. We show that by integrating the constraints of the Constraint theory of conceptual combination and prioritizing the knowledge available within a concept's representation, PUNC can not only generate interpretations that reflect those produced by people, but also mirror the differences in processing times for understanding familiar, similar and novel word combinations.