Doppler radio tracking of the Galileo probe-to-orbiter relay, previously analyzed for its in situ measure of Jupiter's zonal wind at the equatorial entry site, also shows a record of significant residual fluctuations apparently indicative of varying vertical motions. Regular oscillations over pressure depth in the residual Doppler measurements of roughly 1--8 Hz (increasing upward), as filtered over a 134 sec window, are most plausibly interpreted as gravity waves, and imply a weak, but downward increasing static stability within the 5--20 bar region of Jupiter's atmosphere. A matched extension to deeper levels of an independent inertial stability constraint from the measured vertical wind shear at 1--4 bars is roughly consistent with a static stability of ~0.5 K/km near the 20 bar level, as independently detected by the probe Atmospheric Structure Instrument. ¿ 2001 American Geophysical Union