Hot gas dominates the emission in X-ray-luminous early-type galaxies, but i
n relatively X-ray-faint systems, integrated X-ray emission from discrete s
tellar-like sources is thought to be considerable, although the amount of t
he contribution is controversial. To help resolve this issue, we examine th
e radial X-ray surface brightness distribution of 17 X-ray-faint galaxies o
bserved with the ROSAT HRI and PSPC. We assume that the stellar contributio
n follows a de Vaucouleurs law while the hot gas component follows a King b
eta model. For some galaxies, both models Dt equally well, but for a number
of systems, a dual component model yields the best Dt, from which upper bo
unds are placed on the stellar contribution. Best-Dt values for the stellar
contribution are inconsistent with (lower than) that suggested by Fabbiano
, Gioia, & Trinchieri and estimated from the bulge of M31 but are consisten
t with the Forman, Jones, & Tucker estimate of the stellar fraction in X-ra
y-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(-1) L-.(-1).