A medical cauterization snare includes a tubular member such as a catheter, a rod or wire disposed at least partially inside the tubular member, and a resilient loop of a first size attached to a distal end of the rod or wire. The loop includes a nose on a side of the loop opposite the wire. The loop further includes two loop sections each extending between the wire and the nose. The loop sections are each formed with a respective notch or dent for enabling a use of the loop in a second size smaller than the first size. Positioning the loop relative to the tubular member so that the notches or dents are disposed at a mouth opening of the tubular member generates this secondary deployment configuration.