Disclosed exemplary solid state light fixtures use optical cavities to combine or integrate light from LEDs or the like. In such a fixture, the cavity is formed by a light transmissive structure having a volume, and a diffuse reflector that covers a contoured portion of the structure. A circuit board has flexible tabs mounting the light emitters. A heat sink member supports the circuit board and is contoured relative to the shape of the light transmissive structure so that the tabs bend and the emitters press against a sufficiently rigid periphery of the light transmissive structure. TIM may be compressed between the heat sink member and the opposite surface of each tab. Various contours/angles of the periphery of the light transmissive structure and the mating portion of the heat sink member may be used.