We study the optimal contract choice of an upstream monopolist producing an essential input that may sell to two vertically differentiated downstream firms. The upstream supplier can offer an exclusive contract to one of the firms or non-exclusive contracts to both firms. Each of the latter can be made contingent or not on the breakdown of the negotiations between the upstream supplier and the rival downstream firm. The distribution of bargaining power during the contract terms negotiations is the main driving force of the monopolist's choices. A powerful supplier always opts for an exclusive contract. By contrast, a weaker supplier offers non-exclusive contracts and makes each of them contingent or non-contingent such as to guarantee the most favorable outside option in its negotiations. Our main results hold under an horizontally differentiated downstream market too.