Snake-like flexible manipulators are widely used in minimally invasive surgery (MIS), which require adequate dexterity in confined workspace. Typically, the design mechanisms of these manipulators include tendon-driven mechanism and concentric tube mechanism. Though, the workspace and dexterity of these designs are limited due to the lack of control in either the length of the bending section or the curvature of the bending section at the distal end. In this paper, we present a novel constrained wire-driven flexible mechanism (CWFM), in which both the length and the curvature of the bending section are controllable. The idea is to employ an active constraint to control the length of the bending section and use the wires to control the curvature of the bending section. Compared to the existing designs based on wire-driven flexible mechanism (WFM), CWFM has expanded workspace and enhanced dexterity while its size is not sacrificed. Additional benefits include much reduced sweeping area and controllable stiffness. Based on the computer simulation, on average, CWFM with the same size as WFM can improve the dexterity by 4.69 times and reduce the sweeping area to 20.5%.