Significance The structure of the carboxysome resembles a viral capsid, but, unlike many viruses, the monomers of its shell do not appear to fit together in a uniquely preferred way. As a result, the size and shape of this bacterial microcompartment must be determined by the dynamics of its self-assembly process. Using theory and simulation of a model system, we show that the mechanism of assembling such a structure can proceed through nonequilibrium dynamics that are both reliable and controllable. We identify experimentally tunable parameters that modulate the shape and size of the assembled structure, advancing strategies to repurpose natural microcompartments and to create synthetic mimics. , Cyanobacteria sequester photosynthetic enzymes into microcompartments which facilitate the conversion of carbon dioxide into sugars. Geometric similarities between these structures and self-assembling viral capsids have inspired models that posit microcompartments as stable equilibrium arrangements of the constituent proteins. Here we describe a different mechanism for microcompartment assembly, one that is fundamentally nonequilibrium and yet highly reliable. This pathway is revealed by simulations of a molecular model resolving the size and shape of a cargo droplet and the extent and topography of an elastic shell. The resulting metastable microcompartment structures closely resemble those of carboxysomes, with a narrow size distribution and faceted shells. The essence of their assembly dynamics can be understood from a simpler mathematical model that combines elements of classical nucleation theory with continuum elasticity. These results highlight important control variables for achieving nanoscale encapsulation in general and for modulating the size and shape of carboxysomes in particular.