In iterative image restoration, the total variation (TV) norm is the most common regulator to control noise and enforce sharp edges in the images. This paper proposes an exponential version of the TV norm. This exponential version of the TV norm behaves similar to the Lp norm for 0 < p < 1 and it promotes sharp image edges better than the TV norm. This exponential TV is easy to implement. We use computer simulations to compare the effectiveness of preserving sharp edges by the TV regulator and by its exponential version. The image restoration task is image denoising. The exponential regulator is demonstrated by computer simulations as more effective in obtaining piecewise-constant images than the popular TV regulator.