A project requires an initial specific investment. The toatl cost of the project depends on the probability that the supplier will experience a delay in the production schedule. This probability is the supplier's private information. The buyer wouls like to hire a supplier with a low probability of delay. However, it can offer a screening contract only by committing to terminate the project if the supplier is not able to complete it within the original budget limits. We show that cost observability may prevent the buyer from terminating a cost overrun project and this, in turn, prevents screening out bad suppliers. Thus, we provide an example in which superior monitoring ability represents a disadvantage for the buyer. This finding contrast with the common argument that better monitoring represents an advantage of integrated organizations.