We report on the improved ephemerides for the irregular Jovian satellites. We used a combination of numerically integrated equations of motion and a weighted least-squares algorithm to fit the astrometric measurements. The orbital fits for 59 satellites are summarized in terms of state vectors, post-fit residuals, and mean orbital elements. The current data set appears to be sensitive to the mass of Himalia, which is constrained to the range of GM = 0.13-0.28 km3 s-2. Here, GM is the product of the Newtonian constant of gravitation, G and the body's mass, M. Our analysis of the orbital uncertainties indicates that 11 out of 59 satellites are lost owing to short data arcs. The lost satellites hold provisional International Astronomical Union (IAU) designations and will likely need to be rediscovered.