This paper studies the pricing of “private information”, that is information which is of value only (or mainly) for a specific consumer. In private information markets, firms are familiar with their client’s decision problem and consumers purchase information sequentially from firms. As such, the utility for a second opinion depends on the content of the first opinion. This path-dependent nature of the demand has important implications for pricing because firms have to anticipate in which order will their products be considered/ purchased. In particular, firms have the opportunity to specialize in selling first or second opinions only. Empirical evidence on pricing in a variety of private information markets shows that special “second opinion services” exist in some, but not all private information markets. In view of this evidence, the general question that the paper asks is: How should sellers of private information price their products? In particular, when can (will) they specialize in selling first or second opinions only? The goal of the paper is (1) to shed some light on the empirical evidence on pricing in private information markets and (2) to help understand information sellers’ incentives, thereby providing normative insights. Using an analytic model with two firms selling information to Bayesian consumers, we show that under some conditions, firms engage in what we call “temporal differentiation”. Specifically, the higher quality firm prices above the value of information while the lower quality firm charges exactly the value of information. As a result, the lower quality firm sells a first opinion to all consumers whose prior has been contradicted. In this way, the lower quality firm effectively screens the market for the higher quality firm which ends up making more profit than it it were a monopolist. We also point to conditions under which firms are not willing (or able) to differentiate and rather choose to compete for selling either first or second opinions. We relate to findings to real-life examples from a number of professional consulting services including medical, financial/accounting, legal, engineering and marketing advice. The results are also compared to previous work on static markets of public information.