In this paper, we consider the privatization of State-Owned Enterprises (SOEs) that are legal monopolies but not natural monopolies; their markets can be opened to competition once privatization takes place and other competitors can emerge and compete successfully against them in a few years. But until that happens, these privatized SOEs can have a significant level of market power. The currently used "Revenue Maximization (RM)" privatization scheme maximizes the government revenue from privatization but does not provide sufficient incentives for the privatized SOE eiher to charge a price lower than the monopoly price or to improve production efficiency until competition arises. We propose a new scheme to privatize such SOEs. We term this new scheme the "Welfare Maximization (WM)" scheme. The WM scheme practically yields no revenue to the government from the privatization of any such SOE; however, it induces the privatized SOE to charge a competitive price in the absence of any regulation. It also turns out that the WM scheme provides greater incentives for post-privatization process invention (i.e., for post- privatization cost reduction) than RM scheme.