We derive deconvolution equations - dirty map and dirty beam - without
use of Fourier transforms. We thus avoid interpolation of observed co
mplex visibilities (CVs) as well as aliasing effects. MIM (= minimum i
nformation method) implies the modification of the dirty beam such tha
t a straightforward deconvolution without constraints gives a smoothed
result. Smoothing can be diminished at edges and paint sources by mod
ification of the dirty map near these features. We give test examples
in which we discuss in detail the Gibbs phenomenon encountered in any
smoothed deconvolution of sharp features. Finally, we deconvolve old V
LBI observations of 3C 309.1.