A technique is developed for optimally determining a base geopotential field, on which stratospheric heights may be constructed from remotely sensed temperatures. The scheme employs height information from within as well as below remote observational levels. In addition to producing best-estimate height fields within the observational volume, the procedure also yields the optimal level on which to base remotely derived thicknesses. The technique is demonstrated to yield an unbiased and optimal (in the sense of minimized rms error) estimate of the height at levels where conventional errors are typically large. A significant reduction in the rms error is achieved within the sample volume, most notably in cases where the conventional height error grows rapidly in the vertical. At levels where the conventional error has diverged, say due to sparsity in conventional observations, the error in the estimate remains at respectable values. The scheme is thus an effective means of ‘securing’ a reasonable height field at levels where conventional errors may be unacceptable.