Context: GeV gamma-ray pulsations from over 140 pulsars have been characterized using the Fermi Large Area Telescope, enabling improved understanding of the emission regions within the neutron star magnetospheres, and the contributions of pulsars to high energy electrons and diffuse gamma rays in the Milky Way. The first gamma-ray pulsars to be detected were the most intense and/or those with narrow pulses. Aims: As the Fermi mission progresses, progressively fainter objects can be studied. In addition to more distant pulsars (thus probing a larger volume of the Galaxy), or ones in high background regions (thus improving the sampling uniformity across the Galactic plane), we detect pulsars with broader pulses or lower luminosity. Adding pulsars to our catalog with inclination angles that are rare in the observed sample, and/or with lower spindown power, will reduce the bias in the currently known gamma-ray pulsar population. Methods: We use rotation ephemerides derived from radio observations to phase-fold gamma rays recorded by the Fermi Large Area Telescope, to then determine the pulse profile properties. Spectral analysis provides the luminosities and, when the signal-to-noise ratio allows, the cutoff energies. We constrain the pulsar distances by different means in order to minimize the luminosity uncertainties. Results: We present six new gamma-ray pulsars with an eclectic mix of properties. Three are young, and three are recycled. They include the farthest, the lowest power, two of the highest duty-cycle pulsars seen, and only the fourth young gamma-ray pulsar with a radio interpulse. We discuss the biases existing in the current gamma-ray pulsar catalog, and steps to be taken to mitigate the bias.Read less <