We consider incomplete pairwise comparison matrices and determine exactly when they have a consistent completion and, if not, when they have a nearly consistent completion. We use the maximum 3-cycle product as a measure of inconsistency and show that, when the graph of the specified entries is chordal, a completion in which this measure is not increased is always possible. Methodology to produce such completions is developed. Such methodology may also be used to reduce inconsistency with few changes of comparisons.