A guidable, or steerable, or deflectable catheter is provided that includes a proximal portion and a distal portion for insertion into a body cavity. A selectively deflectable segment having an anisotropic bending stiffness for deflection in individual planes is incorporated into the distal portion of the catheter shaft. Upon actuation of pull wires, the distal deflectable segment may be deflected to move/sweep the distal catheter tip through a sweeping plane. The anisotropic bending stiffness of the distal deflectable segment permits in-plane movement of the distal catheter tip in the sweeping plane while resisting any out-of-plane movements. In one arrangement, stiffening elements are selectively disposed within the distal deflectable segment such that the out-of-plane bending stiffness is largely increased and greater than the in-plane bending stiffness for deflection in the sweeping plane. In another arrangement, the cross section of a distal deflectable segment is altered to produce anisotropic area inertias of moment about its centroidal axes, and thus anisotropic bending stiffnesses.