A method includes providing an input signal identifying a desired brightness for one or more LEDs to first and second parallel control paths. The method also includes generating a digital modulation control signal using the first control path, generating a current control signal using the second control path, and driving the one or more LEDs using the control signals. The method further includes performing compensation in at least one of the control paths to compensate for an increased efficiency of the one or more LEDs. Generating the control signals could include (i) adjusting the digital modulation control signal while maintaining the current control signal at a substantially constant value for a range of lower LED brightness values and (ii) adjusting the current control signal while maintaining the digital modulation control signal at a maximum value or within a range of maximum values for a range of higher LED brightness values.