We present experimental studies of inverted-corona targets as neutron sources at the OMEGA Laser Facility and the National Ignition Facility (NIF). Laser beams are directed onto the inner walls of a capsule via laser-entrance holes (LEHs), heating the target interior to fusion conditions. The fusion fuel is provided either as a wall liner, e.g., deuterated plastic (CD), or as a gas fill, e.g., D2 gas. Such targets are robust to low-mode drive asymmetries, allowing for single-sided laser drive. On OMEGA, 1.8-mm-diameter targets with either a 10-μm CD liner or up to 2 atm of D2-gas fill were driven with up to 18 kJ of laser energy in a 1-ns square pulse. Neutron yields of up to 1.5 × 1010 generally followed expected trends with fill pressure or laser energy, although the data imply some mix of the CH wall into the fusion fuel for either design. Comparable performance was observed with single-sided (1x LEH) or double-sided (2x LEH) drive. NIF experiments tested the platform at scaled up dimensions and energies, combining a 15-μm CD liner and a 3-atm D2-gas fill in a 4.5-mm diameter target, laser-driven with up to 330 kJ. Neutron yields up to 2.6 × 1012 were measured, exceeding the scaled yield expectation from the OMEGA data. The observed energy scaling on the NIF implies that the neutron production is gas dominated, suggesting a performance boost from using deuterium-tritium (DT) gas. We estimate that neutron yields exceeding 1014 should be readily achievable using a modest laser drive of ∼300 kJ with a DT fill.