Moment closures of the Boltzmann equation offer the promise of affordable models for the description of non-equilibrium gas flows that take the form of first-order balance laws. They can be seen as natural extensions of traditional methods for continuum-regime gas-flow description. Unfortunately, traditional closures either suffer from a lack of robustness or excessive computational expense. The original closures, developed by Grad, are not robustly hyperbolic due to the possibility for the flux Jacobian to develop complex eigenvalues for states arbitrarily close to local equilibrium. The maximum-entropy closures are globally hyperbolic, but present an excessive computational expense, due to the numerical solution of an entropy-maximization problem needing to be solved for every flux evaluation. Recently, Fox and Laurent have discovered a new hierarchy of quadrature-based moment methods for a one-dimensional gas that remain both robustly hyperbolic and affordable. Fox and Laurent provide closures for any odd number of moments. This presentation shows an alternative method of finding the Fox-Laurent closures, as well as other families of similar closures. The technique also ``fills in the gaps'' and provides equivalent closures for even numbers of moments. Comparisons of resulting models are made for Riemann problems and high-Mach-number shock waves. Applications to plasma flows are also shown. Finally, techniques for the extension of the models to three-dimensional gases are explored.