In various embodiments, lighting systems include an electrically insulating carrier having a plurality of conductive elements disposed thereon, a light-emitting array, and at least one power source. The light-emitting array is disposed over the carrier and includes a plurality of light-emitting strings, each light-emitting string comprising a plurality of electrically connected light-emitting diodes (LEDs). Each LED has at least two electrical contacts, and each electrical contact is electrically connected to a conductive element. The power source provides power to the light-emitting strings.