We argue that both the positron fraction measured by PAMELA and the peculiar
spectral features reported in the total electron-positron (e+e-) flux measured
by ATIC have a very natural explanation in electron-positron pairs produced by
nearby pulsars. While this possibility was pointed out a long time ago, the
greatly improved quality of current data potentially allow to reverse-engineer
the problem: given the regions of pulsar parameter space favored by PAMELA and
by ATIC, are there known pulsars that explain the data with reasonable
assumptions on the injected e+e- pairs? In the context of simple benchmark
models for estimating the e+e- output, we consider all known pulsars, as listed
in the most complete available catalogue. We find that it is unlikely that a
single pulsar be responsible for both the PAMELA e+ fraction anomaly and for
the ATIC excess, although two single sources are in principle enough to explain
both experimental results. The PAMELA excess e+ likely come from a set of
mature pulsars (age ~ 10^6 yr), with a distance of 0.8-1 kpc, or from a single,
younger and closer source like Geminga. The ATIC data require a larger (and
less plausible) energy output, and favor an origin associated to powerful, more
distant (1-2 kpc) and younger (age ~ 10^5$ yr) pulsars. We list several
candidate pulsars that can individually or coherently contribute to explain the
PAMELA and ATIC data. Although generally suppressed, we find that the
contribution of pulsars more distant than 1-2 kpc could contribute for the ATIC
excess. Finally, we stress the multi-faceted and decisive role that Fermi-LAT
will play in the very near future by (1) providing an exquisite measurement of
the e+e- flux, (2) unveiling the existence of as yet undetected pulsars, and
(3) searching for anisotropies in the arrival direction of high-energy e+e-.Comment: revised version, references and new figures added, changes in the
discussion and figure