© 2015 Elsevier B.V. Advances in decision analysis have seen the oil and gas sector adapt its approach to project evaluation and selection through the inclusion of the principles of modern portfolio theory (MPT). Several studies have highlighted how MPT can be applied to optimise a portfolio of upstream oil and gas projects. This provides a useful framework for E&P managers who are seeking to identify the combination of projects that lie on the efficient frontier, where portfolios are structured to maximise total return for a given level of risk. This paper builds on previous research undertaken in this area. It expands the investment set and incorporates real life constraints associated with the available capital budget and investment size in the portfolio optimisation. These are not considered in traditional Markowitz portfolio theory and are typically overlooked in its application within the upstream oil and gas sector. Producing projects are significantly de-risked relative to exploration projects. While their standard deviation is not absolutely zero, producing projects have significantly lower variability in their returns than exploration projects, and can be likened to risk-free assets. Their inclusion in the portfolio optimisation results in the construction of a capital market line (CML) that dominates over portfolios along the efficient frontier. The subsequent introduction of the available capital budget and investment size constraints is shown to modify the CML, and we introduce the concept of a 'Limited CML'. Unlike the CML or traditional efficient frontier, not all portfolios along this curve are efficient. Instead, efficient portfolios are only observed up to a given level of risk (referred to as the 'vertex'). Beyond this level, additional risk is no longer value-accretive, and the expected return for these portfolios can be replicated by portfolios with lower standard deviations. Following construction of the 'Limited CML', a single preferred portfolio can be identified through the application of preference decision theory. We demonstrate how a company's risk tolerance can be quantified for the purpose of constructing certainty equivalent curves. By overlaying these curves with the 'Limited CML' it is possible to identify a single preferred portfolio of E&P assets that is not only efficient, but also matches the targeted risk tolerance.