Active contours that evolve in ultrasound images under gradient descent are often trapped in spurious local minima. This paper presents an evolution strategy called tunneling descent, which is capable of escaping from such minima. The key idea is to evolve the contour by a sequence of constrained minimizations that move the contour in to, and out of, local minima. This strategy is an extension of classical gradient descent. Because tunneling descent does not terminate at a local minima an explicit stopping rule is required. Model-based and model-free stopping rules are presented and formulae for choosing the stopping threshold are given. The algorithm is used to segment the endocardium in 44 short axis cardiac ultrasound images. The energy function of the active contour is derived from a m.a.p. formulation. All segmentations are achieved without tweaking either the energy function or numerical parameters. Experimental evaluation of the segmentations show that the algorithm overcomes multiple local minima to find the endocardium. The accuracy of the algorithm is comparable to that of manual segmentations and significantly better than classical gradient descent active contours. The sensitivity of the segmentation to initialization is also evaluated and it is shown that segmentations from quite different initializations are close to each other. Finally, some limitations of the m.a.p. formulation are discussed.