Bias in the market for news is well-documented. Recent research in economics explains the phenomenon by assuming that consumers want to read (watch) news that is consistent with their tastes or prior beliefs rather than the truth. The present paper builds on this idea but recognizes that (i) besides “biased” consumers, there are also “conscientious” consumers whose sole interest is in discovering the truth, and (ii) consistent with reality, media bias is constrained by the truth. These two factors were expected to limit media bias in a competitive setting. Our results reveal the opposite. We find that media bias may increase when there are more conscientious consumers. However, this increased media bias does not necessarily hurt conscientious consumers who may be able to recover more information from multiple media outlets the more the outlets are biased. We discuss the practical implications of these findings for media positioning, media pricing, media planning, and the targeting of advertising.