Can we do exact and tractable inferences in Mallows-like models for incomplete data? I will show that the answer is yes for the most general form Mallows-type model and a large class of partial orders known as partial rankings (including special cases like top-t rankings). I will also demonstrate that despite partial rankings lacking a sufficient statistic, exact inference is possible with overhead that is at most polynomial in O(nN) and that, in practice, the overhead per data point is negligible. This talk will present algorithms for fitting Recursive Inversion Models and calculating marginal probabilities from partial rankings, as well as discuss results from fitting these models to a wide range of partially ranked data.