Projection data that are limited in number and range of viewing angle cannot completely specify an arbitrary source function. In the space of all permissible functions there exists a null subspace about which the projection measurements provide no information. Deterministic reconstruction algorithms usually set the null space contributions to zero leading to severe reconstruction artifacts. A Fit And Iterative Reconstruction (FAIR) method is proposed that incorporates a priori knowledge of the approximate functional form of the source. In FAIR the parameters of this functional model are determined from the available projection data by a weighted fitting procedure. The resulting distribution is then iteratively revised to bring the final estimate into agreement with the measured projections using a standard algorithm such as ART.