We analyze credence goods markets in the case of two firms. Consumers know that the quality of the good varies but do not know which firm is of high quality. First, we show that the high quality producer may be unable to monopolize the market, or even to survive in some cases, in situations where it is efficient and trusted by all consumers. Second, although a label restoring full information improves welfare, it may also reduce both firms’ profits by intensifying competition. Since even the high quality producer may not wish to label its product, in such cases the label must be mandatory. Third, an imperfect label which moves everybody’s beliefs closer to the truth without restoring full information may produce adverse results on market structure and welfare, either by increasing or by reducing the variance of beliefs.