Individuals typically differ in their identities—the behaviors they deem ideal for themselves and for the members of their network—and in their tolerance for behaviors that deviate from their ideals. This paper studies compromise—that is, departures from one’s ideal point, to be accepted by others. I show that an individual’s compromise in equilibrium is bounded by the difference between her tolerance level and the lowest tolerance level in society. Relatively intolerant individuals, who serve as “bridges,” are critical for reciprocated compromise. When individuals with extreme identities are systematically less tolerant, societies polarize. In contrast, intolerance among moderates encourages cohesion.