  We propose a new Planetary Nebula Luminosity Function (PNLF) that includes
two populations in the distribution. Our PNLF is a direct extension of the
canonical function proposed by Jacoby et al. (1987), in order to avoid problems
related with the histogram construction, it is cast in terms of cumulative
functions. We are interested in recovering the shape of the faint part of the
PNLF in a consistent manner, for galaxies with and without a dip in their PN
luminosity functions. The parameters for the two mode PNLF are obtained with a
genetic algorithm, which obtains a best fit to the PNLF varying all of the
parameters simultaneously in a broad parameter space. We explore a sample of 9
galaxies with various Hubble types and construct their PNLF. All of the
irregular galaxies, except one, are found to be consistent with a two-mode
population, while the situation is less clear for ellipticals and spirals.For
the case of NGC\, 6822, we show that the two-mode PNLF is consistent with
previous studies of the star formation history within that galaxy. Our results
support two episodes of star formation, in which the latter is significantly
stronger.
