Observations made by the Michelson Doppler Imager (MDI) and Variability of solar IRradiance and Gravity Oscillations (VIRGO) on the Solar and Heliospheric Observatory (SOHO) and by the ground-based Birmingham Solar Oscillations Network (BiSON) and Global Oscillations Network Group (GONG) have been used in a concerted effort to search for solar gravity oscillations. All spectra are dominated by solar noise in the frequency region from 100 to 1000 μHz, where g-modes are expected to be found. Several methods have been used in an effort to extract any g-mode signal present. These include (1) the correlation of data—both full-disk and imaged (with different spatial-mask properties)—collected over different time intervals from the same instrument, (2) the correlation of near-contemporaneous data from different instruments, and (3) the extraction—through the application of complex filtering techniques—of the coherent part of data collected at different heights in the solar atmosphere. The detection limit is set by the loss of coherence caused by the temporal evolution and the motion (e.g., rotation) of superficial structures. Although we cannot identify any g-mode signature, we have nevertheless set a firm upper limit to the amplitudes of the modes: at 200 μHz, they are below 10 mm s-1 in velocity, and below 0.5 parts per million in intensity. The velocity limit corresponds very approximately to a peak-to-peak vertical displacement of δR/R☉ = 2.3 × 10-8 at the solar surface. These levels which are much lower than prior claims, are consistent with theoretical predictions.