A lighting system comprising: a substantially planar lightsheet; disposed on the lightsheet, first and second spaced-apart power conductors (110, 120) each extending in a first direction; a plurality of light-emitting strings, each light-emitting string comprising a plurality of interconnected light-emitting elements spaced along the light-emitting string, each having a first end electrically coupled to the first power conductor, each having a second end electrically coupled to the second power conductor, and each being oriented in a second direction not parallel to the first direction, wherein the power conductors supply power to each of the light-emitting strings; and a plurality of control elements each electrically connected to at least one light-emitting string each configured to utilize power supplied from the power conductors (110, 120) to control the current to provide a substantially constant current to the at least one light-emitting string to which it is electrically connected, and each configured to be responsive to a control signal to maintain the substantially constant current through the light-emitting elements until instructed to change to a different substantially constant current, wherein the lightsheet is separable, via a cut spanning the first and second power conductors and not crossing a light-emitting string, into two partial lightsheets each comprising one or more light-emitting strings, each comprising one or more control elements, and each comprising portions of the first and second power conductors (110, 120) configured to supply power to and thereby illuminate the one or more light-emitting strings of the partial lightsheet. a substantially planar lightsheet; disposed on the lightsheet, first and second spaced-apart power conductors (110, 120) each extending in a first direction; a plurality of light-emitting strings, each light-emitting string comprising a plurality of interconnected light-emitting elements spaced along the light-emitting string, each having a first end electrically coupled to the first power conductor, each having a second end electrically coupled to the second power conductor, and each being oriented in a second direction not parallel to the first direction, wherein the power conductors supply power to each of the light-emitting strings; and a plurality of control elements each electrically connected to at least one light-emitting string each configured to utilize power supplied from the power conductors (110, 120) to control the current to provide a substantially constant current to the at least one light-emitting string to which it is electrically connected, and each configured to be responsive to a control signal to maintain the substantially constant current through the light-emitting elements until instructed to change to a different substantially constant current, wherein the lightsheet is separable, via a cut spanning the first and second power conductors and not crossing a light-emitting string, into two partial lightsheets each comprising one or more light-emitting strings, each comprising one or more control elements, and each comprising portions of the first and second power conductors (110, 120) configured to supply power to and thereby illuminate the one or more light-emitting strings of the partial lightsheet.