A new method is presented for producing images from incompletely sampled interferometric data. The method, "smear fitting", models the source with a set of basis functions and then convolves each component with an elliptical Gaussian to account for the uncertainty in its shape and location. This produces much sharper resolution for high signal to noise components than CLEAN without harm to low signal to noise features. It also lends itself to using data from multiple polarizations and/or frequencies to obtain an optimum set of images. Physical insight can also be incorporated by changing the choice of basis function(s).

Smear fitting does not require reweighting or even gridding of the data in the production and display of the model, preserving all of the information in the data both in terms of sensitivity and resolution. It is compared to other methods of producing images in radio interferometry. The comparisons are amply illustrated with both real and simulated data. Smear fitting is found to have sharper resolution than CLEAN, without striping or gridding errors. Although it is similar in principle to maximum entropy deconvolution, by using fewer degrees of freedom it avoids "ringing" artefacts around sharp features embedded in smooth emission. Its processing time is competitive with the other methods and best for objects that require many pixels but can be modeled with relatively few components, such as a set of sharp features superimposed on a smoothly varying background.

Two problems of fitting Gaussians to interferometric data are discussed and solved. These improvements in model fitting made it possible to automate smear fitting, and the details of the process are explained. Smear fitting is applied to study the precession of extragalactic radio jets and measure the thickness of the planetary nebula Vy 2-2, and results from those studies are given.