Obtaining high-quality parallel corpora is of paramount importance for training NMT systems. However, as many language pairs lack adequate gold-standard training data, a popular approach has been to mine so-called "pseudo-parallel" sentences from paired documents in two languages. In this paper, we outline some problems with current methods, propose computationally economical solutions to those problems, and demonstrate success with novel methods on the Tatoeba similarity search benchmark and on a downstream task, namely NMT. We uncover the effect of resource-related factors (i.e. how much monolingual/bilingual data is available for a given language) on the optimal choice of bitext mining approach, and echo problems with the oft-used BUCC dataset that have been observed by others. We make the code and data used for our experiments publicly available.