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The question of who should be admitted as lawful permanent residents reflects a core aspect of immigration restrictions, which often prioritize the interests of U.S. citizens. While public opinion in the United States consistently favors immigrants with higher skills, it remains unclear whether immigration policies align with this consensus. This study examines the research question: Are higher skill levels rewarded as expected when immigrants apply for permanent residency? Using administrative records of all high-skilled foreign workers who applied for permanent labor certification—the first critical step in the employment-based Green Card process—reviewed by the Department of Labor between 2014 and 2024 (N = 850,235), this study identifies a phenomenon I refer to as the “skill paradox.” Paradoxically, overqualified foreign workers face systematic penalties: they are not only more likely to be denied labor certification but also experience significantly longer review times, even after controlling for other skill indicators, demographic characteristics, application details, and company-level factors. Findings suggest that this paradox stems from immigration restrictions that, on the one hand, systematically steer high-skilled immigrants into overqualified positions due to the need for work visa sponsorship, while on the other hand, penalize this very overqualification in permanent residency applications. Overqualified immigrants may signal insufficient employer efforts to recruit qualified U.S. workers, prompting stricter scrutiny by the state. These findings highlight how immigration restrictions generate structural inequalities even for highly skilled immigrants traditionally seen as “deserving.”