A conformable covering comprises an outer portion with rigidity to resist movement on the cornea and an inner portion to contact the cornea and provide an environment for epithelial regeneration. The inner portion of the covering can be configured in many ways so as to conform at least partially to an ablated stromal surface so as to correct vision. The conformable inner portion may have at least some rigidity so as to smooth the epithelium such that the epithelium regenerates rapidly and is guided with the covering so as to form a smooth layer for vision. The inner portion may comprise an amount of rigidity within a range from about 1×10−4 Pa*m3 to about 5×10−4 Pa*m3 so as to deflect and conform at least partially to the ablated cornea and smooth an inner portion of the ablation with an amount of pressure when deflected.