Embedded boundary methods (EBMs) are robust solution methods for highly nonlinear fluid-structure interaction (FSI) problems. They suffer, however, some disadvantages because they perform their computations on embedding, nonbody-fitted fluid meshes. In particular, they tend to generate discrete events that introduce discontinuities in the semi-discretization process and lead to numerical solutions that are insufficiently smooth for differentiation with respect to the evolution of a discrete, fluid/structure interface Γ F∕S h . This hinders their application to the gradient-based solution of fluid-structure optimization problems. Discrete events also promote spurious oscillations in the post-processing of time-dependent results computed at Γ F∕S h .z This paper addresses these issues in the context of Finite Volume method with Exact two-material Riemann problems (FIVER), a comprehensive framework for developing EBMs for highly nonlinear, compressible, FSI problems. It revisits the concept of the status of a node of an embedding fluid mesh and introduces that of a smoothness indicator nodal function, to eliminate discrete events and achieve smoothness in the semi-discretization process. It also introduces a moving least squares approach in the loads evaluation algorithm, to suppress spurious oscillations from integral quantities computed on Γ F∕S h . Equipped with these enhancements, FIVER is shown to deliver, for three different FSI applications, smooth results that are differentiable with respect to evolutions of Γ F∕S h .