An upper bound on the rate of apsidal advance in Vela X-1 is determined, taking into account the effect of the red noise in pulse frequency reported by Boynton et al. (1986). A new, more precise mean orbit is computed which provides substantially smaller upper bounds on both the rate of apsidal advance and the rate of change of the orbital period than previous solutions. A new, hybrid method for measuring the rate of apsidal advance is described that uses eclipse observations as well as pulse timing. The new method is potentially as useful as the direct measurement from pulse-timing alone for systems that allow more precise determinations of eclipse ingress and egress than does Vela X-1.