We are determining the hyperbolic three-manifolds with closed totally geodesic boundary of second and possibly also third lowest volume, using the necklace techniques developed from the low cusp area project. This project hit a snag in 2013, when I discovered that a critical retubing argument from the earlier work of Gabai, Meyerhoff, and Peter Milley doesn’t work for three-manifolds with higher genus. In 2016 I discovered a way around this difficulty that actually even obviates some of the technical arguments from this earlier work.