Trace element quantitation with EELS is a powerful tool for providing information about elemental distribution in biological and materials sciences. Linear least squares fit (LSF) to standards of the signal and the background is a widely used method for retrieving small signals superimposed on a large, slowly varying background. Theoretically, for most accurate background fitting, the fitting window should be as large as possible. However, when using a large window, there may be a mismatch between the fine structure of the standard and the measured background, due to instability of the instrument and the experimental conditions and radiation damage. This mismatch, distributed over the entire window, can severely affect the accuracy of the small signal extracted with LSF. To overcome this problem, a small window, slightly larger than the signal is often used. Fig. 1 shows the results of extracting a small Ca signal by using respectively, a large and a small window for fitting an EELS spectrum collected from a specimen containing 26.3 mmol/kg dry weight Ca.