Although a broad range of methods exists for reconstructing population history from genome-wide single nucleotide polymorphism data, just a few methods gained popularity in archaeogenetics: principal component analysis (PCA); ADMIXTURE, an algorithm that models individuals as mixtures of multiple ancestral sources represented by actual or inferred populations; formal tests for admixture such as f3-statistics and D/f4-statistics; and qpAdm, a tool for fitting two-component and more complex admixture models to groups or individuals. Despite their popularity in archaeogenetics, which is explained by modest computational requirements and ability to analyze data of various types and qualities, protocols relying on qpAdm that screen numerous alternative models of varying complexity and find "fitting" models (often considering both estimated admixture proportions and p-values as a composite criterion of model fit) remain untested on complex simulated population histories in the form of admixture graphs of random topology. We analyzed genotype data extracted from such simulations and tested various types of high-throughput qpAdm protocols ("rotating" and "non-rotating", with or without temporal stratification of target groups and proxy ancestry sources, and with or without a "model competition" step). We caution that high-throughput qpAdm protocols may be inappropriate for exploratory analyses in poorly studied regions/periods since their false discovery rates varied between 12% and 68% depending on the details of the protocol and on the amount and quality of simulated data (i.e., >12% of fitting two-way admixture models imply gene flows that were not simulated). We demonstrate that for reducing false discovery rates of qpAdm protocols to nearly 0% it is advisable to use large SNP sets with low missing data rates, the rotating qpAdm protocol with a strictly enforced rule that target groups do not pre-date their proxy sources, and an unsupervised ADMIXTURE analysis as a way to verify feasible qpAdm models. Our study has a number of limitations: for instance, these recommendations depend on the assumption that the underlying genetic history is a complex admixture graph and not a stepping-stone model.