The structure of a sample of high-redshift (z ~ 2), rotating galaxies with high star formation rates and turbulent gas velocities of Delta *s 40-80 km s--1 is investigated. Fitting the observed disk rotational velocities and radii with a Mo et al. (MMW) model requires unusually large disk spin parameters Delta *l d >0.1 and disk-to-dark halo mass fractions of m d 0.2, close to the cosmic baryon fraction. The galaxies segregate into dispersion-dominated systems with 1 <= v max/ Delta *s <= 3, maximum rotational velocities v max<= 200 km s--1, and disk half-light radii r 1/2 1-3 kpc, and rotation-dominated systems with v max> 200 km s--1, v max/ Delta *s>3, and r 1/2 4-8 kpc. For the dispersion-dominated sample, radial pressure gradients partly compensate the gravitational force, reducing the rotational velocities. Including this pressure effect in the MMW model, dispersion-dominated galaxies can be fitted well with spin parameters of Delta *l d = 0.03-0.05 for high disk mass fractions of m d 0.2 and with Delta *l d = 0.01-0.03 for m d 0.05. These values are in good agreement with cosmological expectations. For the rotation-dominated sample, however, pressure effects are small and better agreement with theoretically expected disk spin parameters can only be achieved if the dark halo mass contribution in the visible disk regime (2-3 X r 1/2) is smaller than predicted by the MMW model. We argue that these galaxies can still be embedded in standard cold dark matter halos if the halos do not contract adiabatically in response to disk formation. In this case, the data favor models with small disk mass fractions of m d = 0.05 and disk spin parameters of Delta *l d 0.035. It is shown that the observed high turbulent gas motions of the galaxies are consistent with a Toomre instability parameter Q = 1 which is equal to the critical value, expected for gravitational disk instability to be the major driver of turbulence. The dominant energy source of turbulence is then the potential energy of the gas in the disk.