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Does the hierarchical relationship between the district courts and the courts of appeals influence decision making at the trial level? Do these judges anticipate responses by appellate panels and condition their decisions based on these expectations? Using a sample of district court cases from 1925 to 1996 that were subsequently reviewed by the courts of appeals, and incorporating a strategic choice statistical framework, I discover that the district courts are constrained by the anticipated responses of the appeals courts. However, this conclusion is not apparent if one analyzes the data using traditional maximum likelihood raethods. Only when empirical analyses specifically model underlying strategic relationships does one discover this constraint. If the federal trial judges anticipate a negative response on appeal, then they curtail their ideological influences (the magnitude of influence decreases by approximately one-half). This pattern remains consistent when one examines civil liberties and economic cases, but not for criminal cases. Thus, the hierarchical structure of the federal judiciary appears to exert a significant constraint on the district courts. Keywords: U.S. district courts; U.S. courts of appeals; federal judiciary; trial courts; judicial decision making; precedent; strategic anticipation