Hot gas dominates the emission in X-ray luminous early-type galaxies , but in relatively X-ray faint systems , integrated X-ray emission from discrete stellar-like sources is thought to be considerable , although the amount of the contribution is controversial . To help resolve this issue , we examine the radial X-ray surface brightness distribution of 17 X-ray faint galaxies observed with the ROSAT HRI and PSPC . We assume that the stellar contribution follows a de Vaucouleurs law while the hot gas component follows a King \beta model . For some galaxies , both models fit equally well , but for a number of systems , a dual component model yields the best fit , from which , upper bounds are placed on the stellar contribution . Best-fit values for the stellar contribution are inconsistent with ( lower than ) that suggested by Fabbiano , Gioia , & Trinchieri ( 1989 ) and estimated from the bulge of M31 , but are consistent with the Forman , Jones , & Tucker ( 1985 ) estimate of the stellar fraction in X-ray faint elliptical and S0 galaxies . Our results indicate an upper limit to discrete sources of L _ { X } / L _ { B } = 1.6 \times 10 ^ { 29 } { ergs s } ^ { -1 } / L _ { \odot } .