Several theoretical studies have proposed that, in response to photospheric foot-point motions, current sheets can be generated in the solar corona without the presence of a null point in the initial potential magnetic field. In these analytic models, current sheets form wherever the coronal field dips down and is parallel to the photosphere. A fundamental assumption in these analyses — commonly referred to as the line-tying assumption — is that all coronal field lines are anchored to a boundary surface representing the top of the dense, gas-pressure-dominated photosphere. In theoretical arguments presented elsewhere (Karpen, Antiochos, and DeVore 1989), however, we show that line-tying is not valid for “dipped” coronal fields, and hence that the conclusions of the line-tied models are incorrect. We contend that current sheets will not form if the photosphere-corona interface is represented by a physically valid model. Here we summarize a numerical investigation of the response of a “dipped” potential magnetic field in a hydrostatic-equilibrium atmosphere to shearing motions of the foot points. Our results show that, in the absence of artificial line-tying conditions, a current sheet indeed does not form at the location of the dip. Rather, the dipped magnetic field rises, causing upflows of photospheric and chromospheric plasma.