Solid-state lighting devices including light-emitting diodes (LEDs) and more particularly LED packages are disclosed. A light-altering material may be provided in particular configurations within an LED package to redirect light toward a primary emission direction. The light-altering material may be arranged on any of a first face, a second face, or a plurality of sidewalls of an LED chip in the LED package. In certain embodiments, a lumiphoric material may be arranged on one or more of the sidewalls. A superstrate may be arranged to mechanically support the LED chip from the first face. The light-altering material may be arranged on or dispersed within the superstrate. In certain embodiments, the primary emission direction of the LED package is substantially parallel to the second face of the LED chip in the LED package. An overall thickness or height of the LED package may be less than or equal to 0.25 mm.