We present a new method for using the observed starlight polarization and polarized submm emission to constrain the shapes and porosities of interstellar grains. We present the modified picket fence approximation (MPFA), and verify that it is sufficiently accurate for modeling starlight polarization. We introduce the starlight polarization integral $Pi_{rm obs}$ as a measure of overall strength of the observed polarization of starlight, and the starlight polarization efficiency integral $Phi$ to characterize the effectiveness of different grain types for producing polarization of starlight. The starlight polarization integral $Pi_{rm obs}$ determines the mass-weighted alignment $langle f_{rm align}rangle$ of the grains. Approximating the aligned grains in the interstellar medium as spheroids, we use $Pi_{rm obs}/Phi$ to show that the observed starlight polarization constrains the grains to have a minimum degree of asphericity. For porosity ${cal P}=0$, the minimum axial ratio is $sim$1.4 for oblate spheroids, or $sim$1.8 for prolate spheroids. If the grains are porous, more extreme axial ratios are required. The same grains that produce the starlight polarization are able to provide the observed polarized emission at submm wavelengths, but with further limits on shape and porosity. Porosities ${cal P}>0.75$ are ruled out. If interstellar grains can be approximated by astrodust spheroids, we predict the ratio of 10$mu{rm m}$ polarization to starlight polarization $p_V$: $p(10mu{rm m})/p_V=0.222pm0.026$. For Cyg OB2-12 we predict $p(10mu{rm m})=(2.1pm0.3)%$, which should be observable.
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