In the last decade, combating migrant smuggling has emerged as a top priority for the European Union (EU). The market for smuggling services to the EU is characterized by (i) a dual structure, comprising both a segment of organized criminal cartels and one of smaller, self-employed smugglers, (ii) significant trading frictions, and (iii) the ability of smugglers to set fees. A directed search model is well-suited to analyze this market. Comparative statics on the equilibrium solution, along with numerical simulations, allow for a detailed examination of various policies aimed at reducing irregular migration and disrupting the smuggling business. Results indicate that general-purpose policy measures effectively curb migration but may inadvertently bolster cartel profits by pushing self-employed smugglers out of the market. Conversely, policies that specifically target criminal organizations may increase the number of self-employed smugglers, potentially leading to higher irregular border crossings.