Forecasting the likely cost of construction work before tendering is known as to be a hazardous task. Both underestimates and overestimates may present problems to clients and contractors. Not surprisingly, cost-engineering activities can be stressful for those responsible. Coping with the stresses requires action on the part of the individuals affected and the organizations to which they belong. This paper examines the effect of organizational supports in the process of project estimation through a survey of construction estimation participants in Hong Kong. Using correlation analysis and regression analysis, it is found that: (1) the stressors of autonomy and feedback are directly related to the stress experienced by cost engineers; (2) informal organizational supports (particularly concerning relationship conflict, Type A behavior, work underload, lack of autonomy, and unfair rewards and treatment) are far more effective than formal supports in reducing stress; and (3) lack of autonomy and lack of feedback are predictable variables affecting stress. Cost-engineering managers and supervisors need to carefully distinguish between those who prefer hands-on support and those who prefer hands-off support. A good communication and team decision-making process and a fair reward and treatment system may help establish close relationships among cost engineers in a company and ensure sufficient autonomy to cost engineers and the participants in the estimation process.