An LED light fixture includes a heat-sink body having a circuit-board mounting surface and a circuit board in thermal-contact relationship to the circuit-board mounting surface. The circuit board has an LED-populated area and a surrounding non-LED-populated area such that lateral heat conduction within the circuit board is greater than heat conduction from the circuit board to the circuit-board mounting surface. The fixture may be a low-profile LED light fixture including a base plate which has a substantially planar back surface, a front surface and heat-dissipating surfaces extending forward from the front surface. An LED circuit board and at least one LED power-circuitry unit, which are secured with respect to the front surface adjacent to the heat-dissipating surfaces, do not extend behind the back surface of the base plate.