We present a simple agency model with a revenue-maximizing government and many public officials (agents) in charge of collecting payments from citizens. Agents are of two types, honest and potentially dishonest, with the latter having an inherent propensity to demand bribes from citizens. This propensity may eventually turn into actual (perceived) corruption depending on the strategy pursued by the government. In equilibrium, we derive a non-linear relationship between potential and perceived corruption and, specifically, three distinct policy regimes in which the opportunistic behaviour is curbed, eradicated or tolerated. Different regimes are characterized by different bureaucracy sizes, and we conjecture that low levels of perceived corruption may, in some circumstances, be due to a dilution effect of bribery cases on large numbers of public employees. Some simple descriptive evidence on European regions appears to confirm our theoretical insights.