  Following a resurgence of interest in dilute superconductivity in polar
semiconductors, we perform a variational calculation to probe the existence of
Fr{\"o}hlich bipolarons in these materials. Our solution is capable of
interpolating between the weak- and strong-coupling limits of the
electron-phonon interaction. We predict bipolaron formation in solely the
strong-coupling regime, and we are not aware of any existing materials at these
parameter values. However, imposing an extrinsic electron size constraint to
mimic confinement on the sub-micron scale produces binding in new parts of the
phase diagram, including at weak coupling, within reach of the
near-ferroelectric perovskites.
