A method and device for treating a Chronic Total Occlusion provides a controllable stiffness catheter with a shaft having a stiffness sheath and an access lumen. The device has a stiffness device in a stiff state below a given temperature and in a soft state above the temperature, a temperature-changing device in thermal contact with the stiffness device, the temperature-changing device changing a temperature of the stiffness device below and above the temperature, and a power controller electrically connected to the stiffness device and selectively supplying power to the temperature-changing device to change a stiffness of the stiffness device between the stiff and soft states. A guidewire is moved to a treatment site and the catheter moves along the guidewire up to CTO in its soft state. The catheter stiffens without straightening and, in the stiff state, the catheter or the guidewire is projecting through the CTO.