Broadly neutralizing HIV antibodies (bnAbs) are typically highly somatically mutated, raising doubts as to whether they can be elicited by vaccination. We used 454 sequencing and designed a novel phylogenetic method to model lineage evolution of the bnAbs PGT121-134 and found a positive correlation between the level of somatic hypermutation (SHM) and the development of neutralization breadth and potency. Strikingly, putative intermediates were characterized that show approximately half the mutation level of PGT121-134 but were still capable of neutralizing roughly 40-80% of PGT121-134 sensitive viruses in a 74-virus panel at median titers between 15- and 3-fold higher than PGT121-134. Such antibodies with lower levels of SHM may be more amenable to elicitation through vaccination while still providing noteworthy coverage. Binding characterization indicated a preference of inferred intermediates for native Env binding over monomeric gp120, suggesting that the PGT121-134 lineage may have been selected for binding to native Env at some point during maturation. Analysis of glycan-dependent neutralization for inferred intermediates identified additional adjacent glycans that comprise the epitope and suggests changes in glycan dependency or recognition over the course of affinity maturation for this lineage. Finally, patterns of neutralization of inferred bnAb intermediates suggest hypotheses as to how SHM may lead to potent and broad HIV neutralization and provide important clues for immunogen design.