Exacting requirements, such as high dimensional accuracy, straightness, fatigue characteristics and high strength, must be satisfied for fine wire used as saw wire, discharge machine wire and bonding wire. In this study, the changes in the straightness and the residual stress of a drawn wire after tension straightening and roller leveler straightening were examined experimentally and by a finite element method (FEM). It was clarified that tension straightening is effective not only for improving straightness but also for decreasing the residual stress of a wire. Improved straightness is observed when the applied tensile stress is 70–80% of the wire strength. By tension annealing treatment, extremely high straightness, which cannot be obtained by cold tension straightening, was obtained. Meanwhile, the straightening of less fine wire using a roller leveler has various merits, such as a simple mechanism and a low machine cost. FEM analysis of roller leveler straightening is effective for predicting the straightness and residual stress. Using a roller leveler with a horizontal roller arrangement, the straightness of a drawn wire improves only slightly. In contrast, using a roller leveler with an inclined roller arrangement, the straightness of a drawn wire improves greatly and an almost perfectly straight wire can be obtained.