The presence of speckle in ultrasound images causes many spurious local minima in the energy function of active contours. These minima trap the segmentation prematurely under gradient descent and cause the algorithm to fail. This paper presents a substantially new reformulation of Tunneling Descent, which is a deterministic technique to escape from unwanted local minima. In the new formulation, the evolving curve is represented by level sets, and the evolution strategy is obtained as a sequence of constrained minimizations. The algorithm is used to segment the endocardium in 115 short axis cardiac ultrasound images. All segmentations are achieved without tweaking the energy function or numerical parameters. Experimental evaluation of the results shows that the algorithm overcomes multiple local minima to give segmentations that are considerably more accurate than conventional techniques.