  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 x 10^29 ergs/s/L(solar).
