Recently, Boyle, Jain, Servan-Schreiber, and Srinivasan (EUROCRYPT’25) introduced the notion of simultaneous-message and succinct (SMS) secure computation. In an SMS protocol, after an initial sampling of a common reference string (CRS), two parties—Alice (with a large input) and Bob (with a small input)—can simultaneously exchange encodings of their private inputs and obtain additive shares of the output of a function evaluated over their inputs. The key requirement is succinctness: namely, the size of the CRS and each input encoding grows only poly-logarithmically in the size of Alice’s input and the function output. Boyle et al., and independently Abram, Malavolta, and Roy (STOC’25), constructed SMS for all bounded-depth Boolean circuits from the plain learning with errors (LWE) assumption. In this work, we extend the study of SMS along two new dimensions: Assuming polynomial hardness of LWE (with a sub-exponential modulus-to-noise ratio), we construct reusable two-party SMS for all bounded-depth Boolean circuits with polylogarithmic communication. By additionally assuming indistinguishability obfuscation, we present a generic compiler from reusable two-party SMS to reusable multiparty SMS.