Costly devices are supported atop telescopically extensible masts of theft resistant mounts well suited to be positioned at temporary, often unattended, outdoor locations. An upper component of each mast carries a torque-disconnect coupler that has two relatively turnable elements, including one fixed to the mast, and another that defines a threaded formation extending along an upstanding axis about which the elements are relatively turnable. A costly device can be tightened to the threaded formation, or can be loosened and removed therefrom—but only when an elongate key-like tool is inserted into aligned passages of the two elements to prevent turning of the threaded formation so a costly device tightened onto the formation can be threaded off of the formation. A shroud cloaks the torque-disconnect coupler and has an opening through which the tool must pass to reach the aligned passages.