We present spectral analysis of ASCA observations of the early-type galaxies NGC 720 ( E4 ) and NGC 1332 ( E7/S0 ) with emphasis on constraining the relative contribution to the X-ray emission from hot gas and the integrated emission from X-ray binaries . Single-temperature spectral models yield poor fits to the spectrum ( \chi ^ { 2 } _ { red } \sim 3 ) over the \sim 0.5 - 5 keV energy range . Two-temperature models significantly improve the spectral fits ( \chi ^ { 2 } _ { red } \sim 1.5 ) and have soft-component temperatures and sub-solar abundances consistent with previous ROSAT single-temperature models ( T _ { soft } \sim 0.6 keV , abundances \sim 0.1 ) and hard-component temperatures ( T _ { hard } \gtrsim 3 keV ) consistent with those expected from a discrete component . The soft component dominates the emission in both galaxies , especially in the 0.4 - 2.4 keV band used in previous ROSAT studies : flux ratios are F _ { hard } / F _ { soft } = 0.19 ( 0.16 - 0.45 ) for NGC 720 ( 2 \sigma ) and F _ { hard } / F _ { soft } = 0.31 ( 0.24 - 0.55 ) for NGC 1332 ( 90 \% ) . Combining these spectral results with ROSAT data we updated constraints on the mass distributions for NGC 720 and NGC 1332 . For NGC 720 , which yields the more precise constraints , the ellipticity of the intrinsic shape of the mass is slightly reduced ( \Delta \epsilon _ { mass } \approx 0.05 ) when the discrete component is added , \epsilon _ { mass } \sim 0.4 - 0.6 ( 90 \% ) . The estimates for the total mass increase with increasing discrete flux , and we find that models with F _ { hard } / F _ { soft } = 0.45 , the 2 \sigma upper limit , have masses that exceed by \sim 30 \% - 50 \% those where F _ { hard } / F _ { soft } = 0 .