The conventional method of mapping a smooth field from noisy observations by fitting to a prescribed set of functions using a least-square-misfit criterion does not properly account for observational noise. The alternative procedure of objective mapping (minimum mean square error estimation) requires certain statistical knowledge of the smooth field and this is often unavailable. A method of mapping which removes both these drawbacks is obtained by combining the two procedures. Development of the hybrid elucidates the relationshp between function fitting and objective analysis.