We present spectral analysis of ASCA data of 17 elliptical and 3 lenticular galaxies most of which have high L _ { x } / L _ { B } . Single-temperature models ( MEKAL and Raymond-Smith ) give unacceptable fits ( \chi ^ { 2 } _ { red } > 1.5 ) in most cases and , in agreement with previous studies , give very sub-solar abundances , \langle Z \rangle = 0.19 \pm 0.12 Z _ { \sun } ( MEKAL ) . The spectra for approximately half the sample are better fit with a cooling-flow model which in three cases gives a substantially better fit . The abundances derived from the cooling-flow model are also significantly larger , \langle Z \rangle = 0.6 \pm 0.5 Z _ { \sun } . We empirically tested the reliability of the plasma codes in the Fe-L region and found no evidence for serious problems with the determined temperatures and abundances . Two-temperature models give substantially better fits that are formally acceptable ( \chi ^ { 2 } _ { red } \sim 1.0 ) in all but a few cases . The highest S/N galaxies ( which also have highest L _ { x } / L _ { B } ) have fitted temperatures < 2 keV for both components consistent with each being distinct phases of hot gas . The lowest S/N galaxies ( which also have lowest L _ { x } / L _ { B } ) generally have a hot component with temperature , T _ { H } \ga 5 keV , which is consistent with emission from discrete sources . ( We discuss the origin of these two components from analysis of L _ { x } - L _ { B } and L _ { x } / L _ { B } . ) The abundances of these two-temperature models are approximately solar , \langle Z \rangle = 0.9 \pm 0.7 Z _ { \sun } ( MEKAL ) , consistent with a recent multi-phase model for the evolution of hot gas in ellipticals . Finally , for several galaxies we find evidence for absorption in excess of the Galactic value and discuss its implications .