Trigonometric parallaxes of 16 nearby planetary nebulae are presented, including reduced errors for seven objects with previous initial results and results for six new objects. The median error in the parallax is 0.42 mas, and 12 nebulae have parallax errors of less than 20%. The parallax for PHL 932 is found here to be smaller than was measured by Hipparcos, and this peculiar object is discussed. Comparisons are made with other distance estimates. The distances determined from these parallaxes tend to be intermediate between some short distance estimates and other long estimates; they are somewhat smaller than those estimated from spectra of the central stars. Proper motions and tangential velocities are presented. No astrometric perturbations from unresolved close companions are detected.