When analyzing an unknown by electron-excited energy dispersive X-ray spectrometry, with the entire periodic table possibly in play, how does the analyst discover minor and trace constituents when their peaks are overwhelmed by the intensity of an interfering peak(s) from a major constituent? In this paper, we advocate for and demonstrate an iterative analytical approach, alternating qualitative analysis (peak identification) and standards-based quantitative analysis with peak fitting. This method employs two “tools”: (1) monitoring of the “raw analytical total,” which is the sum of all measured constituents as well as any such as oxygen calculated by the method of assumed stoichiometry, and (2) careful inspection of the “peak fitting residual spectrum” that is constructed as part of the quantitative analysis procedure in the software engine DTSA-II (a pseudo-acronym) from the National Institute of Standards and Technology. Elements newly recognized after each round are incorporated into the next round of quantitative analysis until the limits of detection are reached, as defined by the total spectrum counts.