An eye-mountable device comprising: one or more layers of polymer material defining a body, the body including a first side and a second side extending from a first end to a second end, the first side opposing the second side, the first side curving inwardly toward the second side, the second side curving outwardly away from the first side, the body including an anterior surface and a posterior surface extending from the first side to the second side and from the first end to the second end, the anterior side opposing the posterior side, the posterior surface having a concave shape; the body further including a thickness profile defined by thicknesses from the anterior surf ace to the posterior surface, the thickness profile including a first thickness region having a first thickness range and a second thickness region having a second thickness range, the first thickness region extending along the first side, the second thickness region extending proximately along the second side and is disposed between the second side and the first thickness region, the second thickness range having at least one thickness that is greater than the first thickness range; wherein the body includes a perimeter defined by the first end, the second end, the first side, and the second side, and the second thickness region extends proximately along the perimeter on the outwardly curving second side, from the first end and the second end, and wherein the thickness profile includes a third thickness region having a third thickness range, the third thickness region being disposed between the first thickness region and the second thickness region, the third thickness range including at least one thickness that is greater than the first thickness range, the second thickness range including at least one thickness that is greater than the third thickness range; and bio-interactive electronics disposed in the body, the bio-interactive electronics operable to interact with a biological environment external to the body and to monitor health-related information. one or more layers of polymer material defining a body, the body including a first side and a second side extending from a first end to a second end, the first side opposing the second side, the first side curving inwardly toward the second side, the second side curving outwardly away from the first side, the body including an anterior surface and a posterior surface extending from the first side to the second side and from the first end to the second end, the anterior side opposing the posterior side, the posterior surface having a concave shape; the body further including a thickness profile defined by thicknesses from the anterior surf ace to the posterior surface, the thickness profile including a first thickness region having a first thickness range and a second thickness region having a second thickness range, the first thickness region extending along the first side, the second thickness region extending proximately along the second side and is disposed between the second side and the first thickness region, the second thickness range having at least one thickness that is greater than the first thickness range; wherein the body includes a perimeter defined by the first end, the second end, the first side, and the second side, and the second thickness region extends proximately along the perimeter on the outwardly curving second side, from the first end and the second end, and wherein the thickness profile includes a third thickness region having a third thickness range, the third thickness region being disposed between the first thickness region and the second thickness region, the third thickness range including at least one thickness that is greater than the first thickness range, the second thickness range including at least one thickness that is greater than the third thickness range; and bio-interactive electronics disposed in the body, the bio-interactive electronics operable to interact with a biological environment external to the body and to monitor health-related information.