In the last decade, combating migrant smuggling has emerged as a top priority for the European Union (EU). An idiosyncratic feature of this market is its dual supply-side organization, comprising a small number of criminal cartels and a large mass of self-employed smugglers. Like other criminal activities, this market is characterized by significant trading frictions. This paper develops a directed search model to analyze the equilibrium of the smuggling market and the impact of policies aimed at disrupting it, with particular attention to forced migration flows. Comparative statics and numerical simulations show that general-purpose policy measures effectively curb migration but increase cartel profits, while policies specifically targeting criminal organizations raise the number of self-employed smugglers, leading to higher levels of irregular border crossings. In contrast, a carefully designed policy mix can simultaneously reduce migration flows and weaken cartel profits.