The Queue Inference Engine (QIE) uses queue departure time data over a single congestion period to infer queue statistics. With partial queue-length information, the queue statistics become more accurate and the computational burden is reduced. We first consider the case in which we are given that the queue length never exceeded a given length L. We then consider the more general case in which we are given the times of all L-to-(L + 1) and (L + 1)-to-L queue-length transitions. We present algorithms, parallel to the QIE algorithms,for deriving the queue statistics under the new conditioning information. We also present computational results, comparing both accuracy and computation time, under the QIE and the new algorithms, for several sample runs.