Thin spherical shells filled with a liquid having a low speed of sound ci are known to have enhanced high-frequency backscattering that generally increases with ka and depends on the acoustics refractive index N=c/ci. Here, a is the radius of the sphere. For N between √2 and 2 there is a backscattered two-chord ray with a nonzero impact parameter b. A physical-optics analysis [P. L. Marston and D. S. Langley, J. Acoust. Soc. Am. 73, 1464–1475 (1983)] is applicable except near N of √2 and 2. The present analysis concerns the strong scattering case of N approaching 2 that corresponds to a vanishing value of b. The outgoing wave front is a surface of revolution W≊a4s4−a2s2, where s is the distance from the optic axis and the coefficient a2 vanishes as N approaches 2. For N=2, a novel physical-optics analysis shows the amplitude contribution increases as (ka)1/2 and is proportional to a Pearcy–Fock function. That function is also used in scattering theory for bubbles [C. E. Dean and P. L. Marston, Appl. Opt. 30, 4764–4776 (1991)]. The analysis was confirmed by comparison with the partial-wave series for the case of a neutrally buoyant liquid neglecting any effects of the shell. The analysis shows that while N=2 has no major advantage, there are special aspects of the scattering. [Work supported by ONR.] a)Present address: EXP Group, Inc., 44063 Fremont Blvd., Fremont, CA 94538.