A headrail designed for powered coverings for architectural openings comprises a housing defining an interior that conveniently hides a battery holder, a signal-receiving system, and an electric motor used to adjust the configuration of the covering. The headrail also hides improved hardware for mounting the motor and, in the case of coverings comprising tiltable elements, improved hardware for mounting a tilt rod. Additionally, in the case of coverings comprising tiltable elements, the headrail hides improved hardware for adjustably attaching the tiltable elements to the tilt rod in a manner that prevents over-rotation of the tiltable elements. The battery holder may comprise a battery magazine or a battery carrier removably mounted in the headrail housing. The batteries may be inserted into or extracted from the battery holder through an opening in a bottom wall of the headrail housing. A swingably mounted trap door may selectively cover or uncover the opening. The battery carrier slidingly engages, through the opening in the bottom of the headrail housing, a battery carrier housing that is mounted within the headrail housing. The signal-receiving system includes an exposed signal receiver for receipt of remote-control signals. The present invention also provides a tilt control system with an inexpensive and effective clutch to prevent over-winding of cords onto a control shaft (e.g., a tilt rod) used to control tiltable elements of the covering. The preferred tilt control system also minimizes torque on the motor or other mechanism used to drive the control shaft.