The correlation between emission-line luminosity (L) and profile-width ({sigma}) for HII galaxies provides a powerful method to measure the distances to galaxies over a wide range of redshifts. In this paper, we use SDSS spectrophotometry to explore the systematics of the correlation using the [OIII]5007 lines instead of H{alpha} or H{beta} to measure luminosities and line widths. We also examine possible systematic effects involved in measuring the profile-widths and the luminosities through different apertures. We find that the green L-{sigma} relation, defined using [OIII]5007 luminosities, is significantly more sensitive than H{beta} to the effects of age and the physical conditions of the nebulae, which more than offsets the advantage of the higher strength of the [OIII]5007 lines. We then explore the possibility of mixing [OIII]5007 profile-widths with SDSS H{beta} luminosities using the Hubble constant H_0_ to quantify the possible systematic effects. We find the mixed L(H{beta})-{sigma}_[OIII]_ relation to be at least as powerful as the canonical L-{sigma} relation as a distance estimator, and we show that evolutionary corrections do not change the slope and the scatter of the correlation and, therefore, do not bias the L-{sigma} distance indicator at high redshifts. Locally, however, the luminosities of the giant HII regions that provide the zero-point calibrators are sensitive to evolutionary corrections and may bias the Hubble constant if their mean ages, as measured by the equivalent widths of H{beta}, are significantly different from the mean age of the HII galaxies. Using a small sample of 16 ad-hoc zero point calibrators we obtain a value of H_0_=66.4^+5.0^_-4.5_km/s/Mpc for the Hubble constant, which is fully consistent with the best modern determinations, and which is not biased by evolutionary corrections.