High-pressure bleeding wounds (and other bleeding wounds) may be treated by applying direct pressure directly in the bleeding wound, such as by applying a back pressure in a confined space around and in the wound. Certain substances and articles may be inserted into the wound, and the wound may be enclosed with that substance or article (such as a hemostatic substance, which may be polymeric), by swelling on contact with molecules (such as water molecules in the blood) encountered in the wound, generates the desired pressure to stop or at least reduce the bleeding without the detrimental effects of a tourniquet. Clot-inducing substances may be introduced into the wound contemporaneously with direct pressure application directly in the wound. Compressible and non-compressible wounds are treated. Treatment stops bleeding without producing pressure injury or ischemic damage. Medical devices using this technology are provided, including removable, biodegradable, medic-administrable devices.