We study spectral properties of generalized MIT bag models. These are Dirac operators Hτ (τ ∈R) acting on domains of R3 with confining boundary conditions. Their lowest positive eigenvalue is of special interest, and it is conjectured to be minimal for a ball among all domains with fixed volume. Studying the resolvent convergence of Hτ in the limits τ →±∞, some spectral properties of the limiting operators H±∞ are inherited throughout the parameterization.