Social Entrepreneurship causes increasing debate in the literature and represents a growing enigma for theories of the firm. Beyond the divergences in its definitions, we show that its mission to create "social value" is an identifiable common feature that cannot be satisfactorily described within the main existing theories. Indeed, social entrepreneurship is, by definition, inconsistent with the shareholder primacy advocating for the too narrow only objective of shareholder profit maximization. But it departs also from stakeholder views that focus on the survival of the firm by aligning its interests with discrepant and "overbroad" crucial stakeholders. Outwardly oriented missions in fact necessitate forgetting the dominant "principal-agent"-like settings, even if principals might be carefully and rightfully chosen. We support our arguments with the study of two empirical cases that are successful long-lasting businesses related to social entrepreneurship: John Lewis Partnership and Equal Exchange. These companies have built pioneering custom-made governance systems - ensuring both performance and social fairness - that dispense with standard implicit hypotheses: their clearly explicit mission identifies "beneficiaries" that are distinct from crucial stakeholders, financial contributors, and principals. Instead, the mission becomes a pivotal attribute to explain and design these organisations' structure and mechanisms. Consequently, we delineate three main theoretical and managerial implications of revealing this mission: it lends a strong legitimacy to the directors and officers by clearly defining the boundaries of their discretion, it specifies and justifies the participants' engagement in the management authority, and it calls for new control mechanisms that are fundamentally different from the monitoring systems of principal-agent relationships. Thus our model clarifies the firms' boundaries and escapes the traditional stakeholders' conflicts of interest. We postulate that this model opens an interesting field for future research, both on social and conventional entrepreneurship, and may entail a deep change in managerial and governance techniques that may have reached a dead-end in the recent economic crisis.