Resonance ionization mass spectrometry (RIMS) combines tunable laser spectroscopy with mass spectrometry to provide a high-efficiency means of analyzing solid materials. We previously showed a very high useful yield of 24% for analysis of uranium using three lasers to excite and ionize atoms sputtered from metallic uranium and uranium dioxide. A new resonance ionization scheme using only two lasers achieves a higher useful yield of 38% by accessing both the ground electronic state and a low-lying electronic state of atomic uranium that is significantly populated by sputtering. The major loss channel in analyzing uranium dioxide is the formation of UOx molecules during sputtering. Prebombardment of the surface with 3 keV noble gas ions prior to analysis reduces the surface and results in a sputtered flux with a greatly enhanced proportion of atomic U. This method of surface reduction results in uranium useful yields as high as 6.6% for uranium dioxide analysis, compared to 2% from previous work.