A problem with the use of flexible functional forms is that the estimated functions frequently violate the regularity conditions (eg, monotonicity, concavity) implied by economic theory. Sampling theory methods exist for imposing curvature conditions at all non-negative prices, but such methods may significantly reduce the flexibility properties of the functional forms. Bayesian methods can be used to maintain these flexibility properties, by imposing regularity condtions at a point, at several points, or over the region within the inferences will be drawn. We use this Bayesian approach to estimate a system of cost and input cost-share equationsfor the Australian merino-woolgrowing sector. The imposition of both monotonicity and concavity constraints at several sets of prices leads to sign reversals and significant changes in the magnitudes of a small number of estimated input-price elasticities.