  We report the results of experiments aimed at reducing the major problem with
cooling flow models of rich cluster X-ray sources: the fact that most of the
cooled gas or its products have not been found. Here we show that much of the
X-ray emission usually attributed to cooling flows can, in fact, be modeled by
a power-law component which is indicative of a source(s) other than thermal
bremsstrahlung from the intracluster medium. We find that adequate simultaneous
fits to ROSAT PSPCB and ASCA GIS/SIS spectra of the central regions of ten
clusters are obtained for two-component models that include a thermal plasma
component that is attributable to hot intracluster gas and a power-law
component that is likely generated by compact sources and/or extended
non-thermal emission. For five of the clusters that purportedly have massive
cooling flows, the best-fit models have power-law components that contribute
$\sim$ 30 % of the total flux (0.14 - 10.0 keV) within the central 3
arcminutes. Because cooling flow mass deposition rates are inferred from X-ray
fluxes, our finding opens the possibility of significantly reducing cooling
rates.
