Solid-state lighting devices and more particularly light-emitting devices including light-emitting diodes (LEDs) with light-altering material arrangements are disclosed. LED devices may include light-altering materials that are provided around peripheral sidewalls of LED chips without the need for a supporting submount or lead frame. The light-altering materials may be provided with reduced thicknesses along peripheral sidewalls of LED chips. An exemplary LED device as disclosed herein may be configured with a footprint that is close to a footprint of the LED chip within the LED device while also providing an amount of light-altering material around peripheral edges of the LED chip to reduce cross-talk. Accordingly, such LED devices may be well suited for use in applications where LED devices form closely-spaced LED arrays. Fabrication techniques are disclosed that include laminating a preformed sheet of light-altering material on one or more surfaces of the LED chip.