  Modern (sub)millimeter interferometers, such as ALMA and NOEMA, offer high
angular resolution and unprecedented sensitivity. This provides the possibility
to characterize the morphology of the gas and dust in distant galaxies. To
assess the capabilities of current softwares in recovering morphologies and
surface brightness profiles in interferometric observations, we test the
performance of the Spergel model for fitting in the $uv$-plane, which has been
recently implemented in the IRAM software GILDAS (uv$\_$fit). Spergel profiles
provide an alternative to the Sersic profile, with the advantage of having an
analytical Fourier transform, making them ideal to model visibilities in the
$uv$-plane. We provide an approximate conversion between Spergel index and
Sersic index, which depends on the ratio of the galaxy size to the angular
resolution of the data. We show through extensive simulations that Spergel
modeling in the $uv$-plane is a more reliable method for parameter estimation
than modeling in the image-plane, as it returns parameters that are less
affected by systematic biases and results in a higher effective signal-to-noise
ratio (S/N). The better performance in the $uv$-plane is likely driven by the
difficulty of accounting for correlated signal in interferometric images. Even
in the $uv$-plane, the integrated source flux needs to be at least 50 times
larger than the noise per beam to enable a reasonably good measurement of a
Spergel index. We characterise the performance of Spergel model fitting in
detail by showing that parameters biases are generally low (< 10%) and that
uncertainties returned by uv$\_$fit are reliable within a factor of two.
Finally, we showcase the power of Spergel fitting by re-examining two claims of
extended halos around galaxies from the literature, showing that galaxies and
halos can be successfully fitted simultaneously with a single Spergel model.
