"The number of undocumented immigrants in the United States: Estimates based on demographic modeling with data from 1990-2016" by Fazel-Zarandi, Feinstein and Kaplan presents strikingly higher estimates of the unauthorized immigrant population than established estimates using the residual method. Fazel-Zarandi et. al.'s estimates range from a low or "conservative" number of 16.7 million unauthorized immigrants, to an "average" of 22.1 million, and to a high of 27.5 million. The Pew Hispanic Center estimated the population at 11.3 million in 2016, and the Department of Homeland Security (DHS) estimated it at 12.3 million. The new method shows much more rapid growth in unauthorized immigration during the 1990s and a substantially higher population in 2000 (13.3 million according to their "conservative" model) than Pew (8.6 million) and DHS (8.5 million). In this commentary, we explain that such an estimate for 2000 is implausible, as it suggests that the 2000 Census undercounted the unauthorized immigrant population by at least 42% in the 2000 Census, and it is misaligned with other demographic data. Fazel-Zarandi, Feinstein and Kaplan's model produces estimates that have a 10 million-person range in 2016, far too wide to be useful for public policy purposes; their estimates are not benchmarked against any external data sources; and their model appears to be driven by assumptions about return migration of unauthorized immigrants during the 1990s. Using emigration rates from the binational Mexican Migration Project survey for the illegal border-crosser portion of the unauthorized population, we generate a 2000 unauthorized population estimate of 8.2 million-slightly below Pew and DHS's estimates-without changing other assumptions in the model. We conclude that this new model's estimates are highly sensitive to assumptions about emigration, and moreover, that the knowledge base about emigration in the unauthorized population during the 1990s is not well enough developed to support the model underlying their estimates.