We discuss applications and extensions of a novel branch-and-bound method for performing protein threading (inverse protein folding) with gapped alignment and empirical amino acid pair potentials (e.g., contact potentials, potentials of mean force). The method can be used with a wide variety of protein threading proposals taken from the literature, and admits variable-length gaps and an arbitrary gap score function. We show how this basic method can be used to find the global minimum, enumerate the low-scoring tail of the distribution, find all low-score local minima, and estimate the distribution partition function, mean, standard deviation, segment placement probabilities, and support uniform sampling.