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Fast neutron spectrum space reactors are an appropriate choice for high thermal powers, but for low powers, they need to be large enough to satisfy the excess reactivity requirement while remaining sub-critical when immersed in wet sand and flooded with seawater following a launch abort accident. All Sectored, Compact space Reactors (SCoRe) are fast spectrum reactors. They have a 0.1 mm thick 157Gd2O3 coating on the outer surface of the reactor vessel to reduce the effect of wet sand as a reflector, and 157GdN fuel additive to reduce the effect of thermal neutron fission on the criticality of the flooded reactor following a launch abort event. This paper identifies the SCoRe-S cores with the smallest BeO radial reflector thicknesses which satisfy the reactivity design requirements. These are a cold-clean and hot-clean excess reactivity > $4.00 and $2.00, respectively, at least $1.00 subcritical at shutdown, and when submerged in wet sand and flooded with seawater following a launch abort event. Reducing the radial reflector thickness increases the 157GdN fuel additive but decreases the diameter, and hence the shutdown margin, of the B4C/BeO control drums. The smallest reactor to satisfy the reactivity design requirements is SCoRe-S7, which has a thick BeO radial reflector (15.3 cm), and its mass (425.3 kg) is 21 kg heavier than the next larger SCoRe-S8 core with a thinner BeO reflector of 13.3 cm. The SCoRe-S7 is also 1.5 kg heavier than the SCoRe-S11, with the largest core, but the thinnest radial reflector thickness of 10.7 cm. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]