An important step in mass spectrometry (MS)-based proteomics is the identification of peptides by their fragment spectra. Regardless of the identification score achieved, almost all tandem-MS (MS/MS) spectra contain remaining peaks that are not assigned by the search engine. These peaks may be explainable by human experts but the scale of modern proteomics experiments makes this impractical. In computer science, Expert Systems are a mature technology to implement a list of rules generated by interviews with practitioners. We here develop such an Expert System, making use of literature knowledge as well as a large body of high mass accuracy and pure fragmentation spectra. Interestingly, we find that even with high mass accuracy data, rule sets can quickly become too complex, leading to over-annotation. Therefore we establish a rigorous false discovery rate, calculated by random insertion of peaks from a large collection of other MS/MS spectra, and use it to develop an optimized knowledge base. This rule set correctly annotates almost all peaks of medium or high abundance. For high resolution HCD data, median intensity coverage of fragment peaks in MS/MS spectra increases from 58% by search engine annotation alone to 86%. The resulting annotation performance surpasses a human expert, especially on complex spectra such as those of larger phosphorylated peptides. Our system is also applicable to high resolution collision-induced dissociation data. It is available both as a part of MaxQuant and via a webserver that only requires an MS/MS spectrum and the corresponding peptides sequence, and which outputs publication quality, annotated MS/MS spectra (www.biochem.mpg.de/mann/tools/). It provides expert knowledge to beginners in the field of MS-based proteomics and helps advanced users to focus on unusual and possibly novel types of fragment ions.