Systems and methods are described for stabilizing an eye for an ocular laser procedure while minimizing corneal distortions which can adversely affect a surgical laser beam. For the systems, a patient interface includes a contact element for stabilizing the eye and establishing a conformal interface with the anterior surface of the cornea. More specifically, devices are disclosed which overlay both a central corneal region and a peripheral corneal region. In some embodiments, a first material is used in the contact element to overlay the central corneal region and a second material is used in the contact element to overlay the peripheral corneal region. Typically, the first and second materials differ in terms of hardness and deformability. In another embodiment disclosed herein, a contact element having a viscoelastic material for stabilizing an eye for a laser procedure is described.