Used the integrative complexity coding system to analyze official American and Soviet foreign policy statements concerned with problems that bore directly on American-Soviet relations issued between 1945 and 1983. Time series (ARIMA) and 2-stage least squares analyses revealed that the integrative complexity of Soviet statements was a function of Soviet complexity levels in the past, American complexity levels in the present, Soviet military or political interventions in other countries, the successful culmination of American-Soviet negotiations, and American presidential elections. The integrative complexity of American statements was a function of American complexity levels in the past, Soviet complexity levels in the past, presidential elections, changes in presidential administrations, Soviet military or political interventions in other countries, American military or political interventions in other countries, and the successful culmination of American-Soviet negotiations. Findings are interpreted in terms of 2 complementary levels of analysis: the study of cognitive processes and the study of bargaining and impression management strategies. (77 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)