A reliable free-breathing (FB) cine DENSE method would benefit myocardial strain imaging in many patients. An echo due to T1 relaxation is an important source of artifacts, particularly for free-breathing acquisitions. We propose to optimize suppression of these echoes by minimizing k-space entropy. The method was tested in 10 subjects (6 healthy volunteers and 4 heart failure patients) and compared to a conventional diaphragm navigator method (dNAV). Image reconstruction by minimizing k-space entropy provided better image quality than the conventional dNAV method.