This paper analyzes first-price sealed-bid auctions of standing timber organized by the French forest service, Office National des Forêts (ONF). A feature of these auctions is that they are held with random reserve prices. We consider an auction model with a random reserve price within the independent-private-value paradigm. After establishing the identification of the model, we estimate the underlying bidders' private-value distribution by using a simple two-step nonparametric procedure. This procedure allows the computation of the winners' informational rents as well as the optimal reserve price. We then simulate a first-price sealed-bid auction with the optimal announced reserve price. Empirical results show that the optimal reserve price allows the ONF to extract more of bidders' willingnesses to pay. Moreover, our results show that, though sales do not vary much, profits for the ONF would significantly increase and less timber would be sold.