As the demand for high-resolution gravity gradient data increases and surveys are undertaken over larger areas, new challenges for data processing have emerged. In the case of full-tensor gradiometry, the processor is faced with multiple derivative measurements of the gravity field with useful signal content down to a few hundred meters' wavelength. Ideally, all measurement data should be processed together in a joint scheme to exploit the fact that all components derive from a common source. We have investigated two methods used in commercial practice to process airborne full-tensor gravity gradient data; the methods result in enhanced, noise-reduced estimates of the tensor. The first is based around Fourier operators that perform integration and differentiation in the spatial frequency domain. By transforming the tensor measurements to a common component, the data can be combined in a way that reduces noise. The second method is based on the equivalent-source technique, where all measurements are inverted into a single density distribution. This technique incorporates a model that accommodates low-order drift in the measurements, thereby making the inversion less susceptible to correlated time-domain noise. A leveling stage is therefore not required in processing. In our work, using data generated from a geologic model along with noise and survey patterns taken from a real survey, we have analyzed the difference between the processed data and the known signal to show that, when considering the Gzz component, the modified equivalent-source processing method can reduce the noise level by a factor of 2.4. The technique has proven useful for processing data from airborne gradiometer surveys over mountainous terrain where the flight lines tend to be flown at vastly differing heights.