The correlation between emission-line luminosity (L) and profile-width (σ) 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 Hα or Hβ 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−σ relation, defined using [OIII]5007 luminosities, is significantly more sensitive than Hβ 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 Hβ luminosities using the Hubble constant H0 to quantify the possible systematic effects. We find the mixed L(Hβ) − σ[OIII] relation to be at least as powerful as the canonical L−σ 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−σ 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 Hβ, 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 H0 = 66.4+ 5.0-4.5km s-1 Mpc-1 for the Hubble constant, which is fully consistent with the best modern determinations, and which is not biased by evolutionary corrections.