We consider a dynamic posted-price mechanism of a seller who must sell a single unit of a good to a number of buyers before a deadline. The seller cannot pre-commit to any price-path. Even when the buyers are symmetric (though non-anonymous) to the seller, the seller can charge different prices to different buyers. We show that this asymmetric treatment of symmetric buyers revenue-dominates the optimal symmetric mechanism. We change the random tie-breaking allocation rule, used for symmetric mechanisms, to generate higher revenue for the seller. We show that the result holds even in static environment, though the marginal benefit of price discrimination increases with the time horizon of the game.