Network performance tomography involves correlating end-to-end performance measures over different network paths to infer the performance characteristics on their intersection. Multicast based inference of link-loss rates is the first paradigm for the approach. Existing algorithms generally require numerical solution of polynomial equations for a maximum-likelihood estimator (MLE), or iteration when applying the expectation maximization (EM) algorithm. The purpose of this note is to demonstrate a new estimator for link-loss rates that is computationally simple, being an explicit function of the measurements, and that has the same asymptotic variance as the MLE, to first order in the link-loss rates.