Global models of the extended solar corona, driven by observed photospheric magnetic fields, generally cannot reproduce the amplitude of the measured interplanetary magnetic field at 1 AU (or elsewhere in the heliosphere), often underestimating it by a factor of two or more. Some modelers have attempted to resolve this “open flux” problem by adjusting what they believe to be errors in the estimates of the photospheric field values. Others have simply multiplied interplanetary values by some correction factor to match 1 AU values. Here, investigate whether this “missing” flux can be explained by a source of largely unobserved, concentrated bundles of flux in the photosphere at latitudes too high to be adequately resolved by ground-based observatories or Earth-based spacecraft. Using potential field source-surface and magnetohydrodynamic models, we demonstrate that this additional polar flux can (at least partially) resolve the open flux problem, without generating any new observational discrepancies. The upcoming joint ESA/NASA Solar Orbiter mission should be able to support or refute this idea.