A drape has a longitudinal pocket on one or both sides of the drape. A stabilizer is placed within the pocket and extends the length of the pocket. The stabilizer is supported by a drapery support such as a rod or track in a manner which enables the panel to move along the drapery support from a closed, drawn position to an open, stacked position. The stabilizer is supported by the drapery support and is free to move within the pocket. The stabilizer prevents the drape from flaring at the bottom. A wand may be attached to the stabilizer or to a carrier or other assembly to which the stabilizer is attached.