  The M dwarf Gliese 581 is believed to host four planets, including one (GJ
581d) near the habitable zone that could possibly support liquid water on its
surface if it is a rocky planet. The detection of another habitable-zone
planet--GJ 581g--is disputed, as its significance depends on the eccentricity
assumed for d. Analyzing stellar activity using the H-alpha line, we measure a
stellar rotation period of 130+/-2 days and a correlation for H-alpha
modulation with radial velocity. Correcting for activity greatly diminishes the
signal of GJ 581d (to 1.5 sigma), while significantly boosting the signals of
the other known super-Earth planets. GJ 581d does not exist, but is an artifact
of stellar activity which, when incompletely corrected, causes the false
detection of planet g.
