A light-emitting diode package is described comprising a body including a hollow having a rim that extends outwardly from an open end of the hollow. A light emitting diode is positioned in the hollow and opposite the open end. A nongaseous transparent optical medium fills the hollow and a phosphor-containing element (PCE) is disposed over the hollow sealing the open end. The PCE has a solid body and a lateral portion including a periphery and dividing a top and a bottom. The bottom of the PCE is convex and in contact with the nongaseous transparent optical medium and the periphery of the PCE is in contact with the rim.