Classical homological algebra is built around the class of projective modules. Relative homological algebra attempts to have some other class $\mathcal{C}$ play the role that projectives played in the classical setting. But in order for this to be well-behaved, the $\mathcal{C}$ needs to be a "precovering" class, and an often-used sufficient condition is that $\mathcal{C}$ is "deconstructible (a concept implicit in Eklof-Trlifaj work around 2000, and related to Quillen's Small Object Argument). I will present a "top-down" characterization of deconstructibility in terms of set-theoretic elementary submodels, which allows us to prove new theorems and substantially streamline older proofs.