To understand the origins of complexity in public policy, this paper develops a model of incremental policymaking whereby policy modifications are constrained by backward-dependence: before undoing an older modification, the policymaker must first undo more recent modifications. The analysis focuses on policy outcomes under political conflict. We demonstrate and discuss two mechanisms that result in excessively complex policies. First, complexity may take the form of kludges, i.e., incremental modifications to existing policy that leave fundamental inefficiencies unresolved. Kludges emerge and persist under political conflict between ideologically opposed parties, especially in the presence of frictions that impede policymaking. Second, complexity may be produced by obstructionist behavior, whereby one party deliberately introduces seeming useless policy modifications to impede opponents’ attempts to change policy. We describe how the nature of obstructionism, and the persistence of the resultant complexity, depends on the type of opponent that a policymaker faces.