Abstract:  Since its introduction almost fifty years ago, Mori's Bend-and-Break lemma has been an important tool in birational geometry and the study of curves. There are several different versions, but roughly speaking, the result guarantees the existence of a rational curve of somewhat low degree under certain assumptions on the variety. It has been used in all sorts of contexts, from concretely studying the geometry of specific varieties to the MMP and the classification of Fano varieties. However, the result used up until now is off by a factor of two from the optimal bound we might hope for. In this talk, we describe an improved degeneration technique using the Kontsevich space that allows us to achieve the optimal bound for Bend-and-Break. We then discuss several applications of the stronger bound, including the study of lengths of extremal rays and characterizations of projective space.  This is joint work with Osamu Fujino, Eric Jovinelly, and Brian Lehmann.