Identifying as many gamma-ray pulsars as possible in the Fermi Large Area Telescope (LAT) data helps test pulsar emission models by comparing predicted and observed properties for a large, varied sample with as little selection bias as possible. It also improves extrapolations from the observed population to estimate the contribution of unresolved pulsars to the diffuse gamma-ray emission. We use a recently developed method to determine the probability that a given gamma-ray photon comes from a known position in the sky, convolving the photon’s energy with the LAT’s energydependent point-spread-function (PSF), without the need for an accurate spatial and spectral model of the gamma-ray sky around the pulsar. The method is simple and fast and, importantly, provides probabilities, or weights, for gamma rays from pulsars too faint for phase-integrated detection. We applied the method to over a thousand pulsars for which we obtained rotation ephemerides from radio observations, and discovered gamma-ray pulsations from 16 pulsars, 12 young and 4 recycled. PSR J2208+4056 has spindown power ˙E = 8 × 1032 erg s−1, about three times lower than the previous observed gamma-ray emission “deathline”. PSRs J2208+4056 and J1816−0755 have radio interpulses, constraining their geometry and perhaps enhancing their gamma-ray luminosity. We discuss whether the deathline is an artifact of selection bias due to the pulsar distance.