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Prior research showed that people holding attitudes on relatively moral topics became more open to two- rather than one-sided messages as the moral basis of their attitudes increased. Across three studies (N = 963), we extend this finding to relatively non-moral topics by demonstrating that two-sided messages can encourage people with strong attitudes indexed by various non-moral attitude strength measures to be more open to contrary positions. Study 1 demonstrated this for four indicators of attitude strength (e.g., certainty). As the strength of one’s attitude increased, two-sided messages increased in relative effectiveness over one-sided communication. This was mediated by perceived appreciation for the speaker acknowledging one’s view. Study 2 replicated this finding in a preregistered experiment. Study 3 conceptually replicated and extended it to people holding attitudes based on their political identity …