X-ray absorption spectroscopy (XAS) is one of the most widely used experimental techniques to study the electronic and spatial structure of materials. Fluorescence yield mode is bulk-sensitive, but has several serious problems coming from saturation effects. In this study, we show the usefulness of partial fluorescence yields in addressing these problems. We discuss the different behaviors of La2NiMnO6 and LiMnO2 at the Mn 2p absorption edges. The total fluorescence yield produces misleading spectra for LiMnO2 due to the absence of high-Z (Z: atomic number) elements. We conclude that the measurement of the inverse partial fluorescence yield is essential in studies of LiMnO2, which is a hotly debated Li-ion battery material.