The noise properties of an LED with high quantum efficiency are investigated. Light with sub-Poissonian photon statistics is generated by driving the LED with a high impedance, well regulated current source. It is shown that it is necessary to distinguish between the measured total quantum efficiency and the optical quantum efficiency. In addition, the correlation between the fluctuations in the driving current and the fluctuations in the photocurrent is demonstrated, allowing a suppression of the shot noise after the measurement. The properties of this alternative noise reduction technique are discussed.