Disclosed are methods for securing the intersection formed by two or more crossed strands. The intersection defines at least two sections. The practice of the disclosed methods includes bending a securing material, such as a suture or other suitably biocompatible material, through at least two of the sections formed by the intersection, and joining them to secure the intersection. Also disclosed are devices formed by using securing material to secure the intersection of crossed strands of a medical device, such as a woven stent. The secured intersection or intersections of the resultant device enhance the structural integrity of the device, and may serve to eliminate the possible unwinding or release of unsecured, or free, strand ends. Radiopaque materials, in addition to polymers, may be used as securing material.