A braided structure that includes a core and a sheath is provided. The core includes a yarn formed at least in part from an aromatic polymer (e.g., an aromatic polyester/liquid crystalline polymer or an aramid polymer), and the sheath, which includes a plurality of ultra high molecular weight polyolefin yarns, is braided around the core. The sheath has an overall diameter ranging from about 60 micrometers to about 650 micrometers. Despite its small diameter, the braided structure can be creep resistant and abrasion resistant while at the same time exhibiting low elongation, a high load at break, and high stiffness. The braided structure can be used in medical applications such as sutures, load bearing orthopedic applications, artificial tendons/ligaments, fixation devices, actuation cables, components for tissue repair, etc.