Solid-state lighting devices including light-emitting diodes (LEDs), and more particularly LEDs and packaged LED devices with spacer layer arrangements are disclosed. An LED package may include one or more LED chips on a submount with a light-altering material arranged to redirect light in a desired emission direction with increased efficiency. A spacer layer is arranged in the LED package to cover rough surfaces and any gaps that may be formed between adjacent LED chips. When the light-altering material is applied to the LED package, the spacer layer provides a surface that reduces unintended propagation of the light-altering material toward areas of the LED package that would interfere with desired light emissions, for example over LED chips and between LED chips. In various arrangements, the spacer layer may cover one or more surfaces of a lumiphoric material, one or more LED chip surfaces, and portions of an underlying submount.