Embodiments related to cryogenically ablating a portion of the inner surface of a vessel by constraining a cryoballoon using various apparatuses and methods are disclosed. For example, a catheter can include a cryoballoon for ablation of the vessel wall and a constraining element disposed substantially in parallel with the cryoballoon to deflect or offset a portion of the cryoballoon away from non-target tissue of the vessel wall and prevent ablation of the non-target tissue. Partial circumferential, non-continuous, or helical ablation can be effective for treating a variety of renal, cardio-renal, and other diseases including but not limited to hypertension, heart failure, renal disease, renal failure, contrast nephropathy, arrhythmia, and myocardial infarction. The constraining element may be, for example, a second inflatable balloon or one or more self-expanding prongs.
