We present sub-arcsecond resolution IRAM PdBI interferometry of eight submillimeter galaxies at redshifts from 2 to 3.4, where we detect continuum at 1mm and/or CO lines at 3 and 1 mm. The CO 3-2/4-3 line profiles in five of the sources are double-peaked, indicative of orbital motion either in a single rotating disk or of a merger of two galaxies. The millimeter line and continuum emission is compact; we marginally resolve the sources or obtain tight upper limits to their intrinsic sizes in all cases. The median FWHM diameter for these sources and the previously resolved sources, SMMJ023952-0136 and SMMJ140104+0252 is less than or equal to 0.5" (4 kpc). The compactness of the sources does not support a scenario where the far-IR/submm emission comes from a cold, very extended dust distribution. These measurements clearly show that the submillimeter galaxies we have observed resemble scaled-up and more gas rich versions of the local Universe, ultra-luminous galaxy (ULIRG) population. Their central densities and potential well depths are much greater than in other redshift 2-3 galaxy samples studied so far. They are comparable to those of elliptical galaxies or massive bulges. The SMG properties fulfill the criteria of 'maximal' starbursts, in which most of the available initial gas reservoir of 10^10-10^11 solar masses is converted to stars on a few dynamical timescales.