We consider the variational problem of micromagnetics for soft, relatively small thin films with no applied magnetic field. In terms of the film thickness t, the diameter l and the magnetic exchange length w, we study the asymptotic behavior in the small-aspect-ratio limit t/ l --> 0, when either ( a) w(2)/ l(2) >> ( t/ l)| log( t/ l)| or ( b) w(2)/ l(2) similar to ( t/ l)| log( t/ l)|. Our analysis builds on prior work by Gioia & James and Carbou. The limiting variational problem is much simpler than 3D micromagnetics; in particular it is two-dimensional and local, with no small parameters. The contribution of shape anisotropy reduces, in this limit, to a constant times the boundary integral of ( m center dot n)(2).