The procurement of public construction projects must walk a fine line between the corruption of state officials and collusion of contractors. The method of awarding projects to the lowest responsible tenderer was originally implemented to guard against corruption of state officials. However, an investigation of the construction industry in the Canadian province of Quebec showed that lowest-tender-offer procurement gave rise to collusion of companies tendering for the contracts. Alternatively, best-value procurement has been used for decades, but here problems arise owing to the necessity of subjective judging of measures other than price to compare bids, giving rise to time- and money-consuming protests. The paper proposes a compelling argument that the construction engineering management (CEM) culture should refocus its efforts on enhancing project cost certainty rather than merely searching for means to design a project in a manner that produces the lowest initial cost, and awards the construction to the lowest tender offer that focuses on cost savings during the project development and delivery process. The difference in the two approaches is subtle but extremely important. To make the transition, the engineering management tools must be advanced to the next level. This means that all project control tools for managing cost, schedule, and technical scope must be transformed from working in the deterministic mode to the stochastic mode, thus making the probability of completing the project within or below its official budget the primary decision criterion. To do so, CEMs must accept that there is a benefit in paying more for an alternative that increases cost certainty for the entire project. The authors of this paper hope that it will provide the grist for a more general dialog across all industry sectors where engineering management is practiced.