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The bilevel driving technique has realized a 2-D control of the luminosity and emitted color of white LEDs with duty cycle and forward current levels. Unfortunately, various combinations of these dimming control parameters can lead to significant changes in junction temperature, which further modify the luminosity and emitted color of LEDs. In this paper, the theoretical aspects of these complex interactions and the impact of bilevel drive on the color-shift properties of white LEDs are discussed in detail by using a mathematical color-shift model. Two color-shift reduction methods are proposed based on the insights obtained from this model. This study shows that a heat sink's thermal resistance that minimizes the overall color shift over dimming can be uniquely determined from the knowledge of some measurable LED parameters, and gives rise to a global minimum color shift. If such a thermal resistance cannot be realized due to practical limitations, the second method that utilizes an adaptive change of forward current levels over dimming can be adopted. Based on their nature, these methods are classified as stationary and adaptive methods, respectively. Their validity is supported by experimental measurements on a commercial white LED.