The purpose of this paper is to present the advantages of the direct presCrIbed suRface Curvature distribution bLade dEsign (CIRCLE) method for the design of high-efficiency turbomachinery blades. These advantages are illustrated by redesigning several examples of axial turbomachinery blades of interest to energy conversion devices, and discussing in detail the aerodynamic performance and efficiency improvements of the redesigned blades over the original geometries. The two-dimensional (2D) method, originally proposed for turbine blades, has been extended for use with 2D and three-dimensional (3D) turbine, compressor and fan blades, and isolated airfoils. By specification, the method allows joining line segments between the leading edge (LE) and trailing edge (TE) circles or ellipses so that the streamwise distribution of surface curvature and slope of curvature are continuous everywhere from the LE stagnation point to the TE stagnation point. The form of the line segments to prevent the "wiggles" of higher order lines is presented. Also by specification, the CIRCLE method can be integrated with multi-objective heuristic or evolutionary-algorithm optimization methods. The efficacy of the method is examined by: redesigning two 2D turbine blades, one 2D compressor blade, and one 2D isolated airfoil: and by designing one 3D compressor blade row and one 3D turbine blade row. The aerodynamic performance improvements between the original and the sample redesigned blades are discussed in detail, resulting in higher-efficiency blades than the original geometries. Further extension of the method for centrifugal and mixed-flow impeller geometries is a coordinate transformation. It is concluded that the CIRCLE method is a new design environment enabling the original design (or redesign) of high-efficiency 2D and 3D turbomachine blades, with direct applications in a variety of energy conversion devices. (C) 2011 Published by Elsevier Ltd.