The Little map sends reduced decompositions of permutations to standard Young tableaux, bijectively realizing an algebraic approach to enumerating reduced decompositions. I will present joint work with Sara Billey, Austin Roberts and Benjamin Young wherein we demonstrate a Little map for signed permutations and characterize each map in terms of Edelman-Greene insertion and Kraskiewicz insertion, respectively. This leads to new insights about the insertion maps, previously conjectured by Thomas Lam.