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 twelve nebulae have parallax errors less than 20 percent. The parallax for PHL932 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 estimated from spectra of the central stars. Proper motions and tangential velocities are presented. No astrometric perturbations from unresolved close companions are detected.