Compression bandage for a human calf, comprisinga) a first engagement zone on a first major surface, comprising mechanical engagement means,b) a second engagement zone on the first major surface, comprising mechanical engagement means,c) a soft section between the first and the second engagement zone, having a reduced modulus of elasticity in length direction,d) a stiff section having an elevated modulus of elasticity in length direction, and having a length greater than the length of the soft section.The stiff section comprises a third engagement zone on the second major surface, comprising mechanical engagement means, for engagement with the first and with the second engagement zone. When wrapping the bandage around the calf, the third engagement zone can engage, in a subsequent turn, with the first engagement zone, and with the second engagement zone, so that the stiff section bridges the soft section.The disclosure also provides a kit comprising a compression stocking and a stiffening wrap.