  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 energy-dependent 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 Edot = 8e32 erg/s, 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.
