While heavy lexical borrowing can pose a problem to any approach to linguistic prehistory, it has often been regarded as an especially difficult problem for lexicostatistics, especially in such areas as Australia, where some believe that extensive borrowing is the norm. The present paper applies lexicostatistics to what is arguably the most massive case of borrowing known for Australia, namely between the Jingulu and Mudburra languages of the Northern Territory, and finds that it actually leads to what is generally considered the correct genetic classification of these languages. This result is then shown to depend on certain relationships among the lexicostatistical percentages that may not always obtain in other cases of heavy borrowing.