A method is developed that removes a priori information from remotely sensed atmospheric state profiles. This consists of a Wiener deconvolution, whereby the required cost function is obtained from the complete data fusion framework. Asserting that the deconvoluted averaging kernel matrix has to equal the unit matrix, results in an iterative process for determining a profile-specific deconvolution matrix. In contrast with previous deconvolution approaches, only the dimensions of this matrix have to be fixed beforehand, while the iteration process optimizes the vertical grid. This method is applied to ozone profile retrievals from simulated and real measurements co-located with the Izaña ground station. Individual profile deconvolutions yield strong outliers, including negative ozone concentration values, but their spatiotemporal averaging results in prior-free atmospheric state representations that correspond to the initial retrievals within their uncertainty. Averaging deconvoluted profiles thus looks like a viable alternative in the creation of harmonized Level-3 data, avoiding vertical smoothing difference errors and the difficulties that arise with averaged averaging kernels.