If a public firm is managed less efficiently than private producers facing similar conditions, then privatisation will increase the overall efficiency of the industry and benefit society. This paper challenges this apparently innocuous conclusion. As long as the private firms' efficiency improves as a result of competition, then it will also be higher when they are subjected to "unfair" competition from a public oligopolist with no budget constraint. We show that it may happen that the loss in efficiency due to the relatively inefficient public firm is more than compensated by gains in the efficiency of the private firms.