The soft bootstrap program aims to construct consistent EFT's by recursively imposing the desired soft limit using on-shell recursion relations. The prime example is the leading two-derivative operator for the SU(N)xSU(N)/SU(N) nonlinear sigma model. We extend the soft boostrap program to four-derivative operators in the EFT, which include the Wess-Zumino-Witten term. Along the way we uncover a new example of soft-bootstrappable EFTs, which involves the SO(N+1)/SO(N) NLSM.