LED packages are disclosed that are compact and efficiently emit light, and can comprise encapsulants with curved and planar surfaces. The packages can comprise a submount with a one or a plurality of LEDs, and in those with a plurality of LEDs each of the LEDs can emit the same or different wavelengths of light than the others. A blanket conversion material layer can be included on at least some of the LEDs and the submount. The encapsulant can be on the submount, over at least some of the LEDs, with each of the planar surfaces being vertical and aligned with one of the edges of the submount. The encapsulant can also have a upper curved surface with a relatively large radius of curvature, with the combination of curved and planar surfaces resulting in efficient emission of light with a relatively narrow emission profile.