Previous studies used techniques from network science to identify individual nodes and a set of nodes that were “important” in a network of phonological word-forms from English. In the present study we used a network simplification process—known as the backbone—that removed redundant edges to extract a subnetwork of “important” words from the network of phonological word-forms. The backbone procedure removed 68.5% of the edges in the original network to extract a backbone with a giant component containing 6,211 words. We compared psycholinguistic and network measures of the words in the backbone to the words that did not survive the backbone extraction procedure. Words in the backbone occurred more frequently in the language, were shorter in length, were similar to more phonological neighbors, and were closer to other words than words that did not survive the backbone extraction procedure. Words in the backbone of the phonological network might form a “kernel lexicon”—a small but essential set of words that allows one to communicate in a wide-range of situations—and may provide guidance to clinicians and researchers on which words to focus on to facilitate typical development, or to accelerate rehabilitation efforts. The backbone extraction method may also prove useful in other applications of network science to the speech, language, hearing and cognitive sciences.