This paper illustrates the improvement gained for a typical analytical near-earth satellite orbit when the J22 and J3 long-periodic perturbations are adjoined to the second-order Izsak-Borchers relations. The standards of comparison were two numerically integrated ephemerides. One standard consisted of the Vinti potential function with only J22 term superposed; the other standard was also the Vinti potential, but with only the J3 term superposed. With reference to the J22 standard, the respective rms fits in position for a 24 h ephemeris were 3.07X 10- earth radii units (eru) for the Izsak equations and only 0.29X 10- eru when the J22 perturbations were included. The corresponding J22 perturbations applied to the velocities resulted in improvement from 3.20X 10-8 eru/sec to 0.53X 10-8 eruIsec. With reference to the J3 standard, the respective rms fits in position were 3.63X 10-8 eru for the Izsak equations and 0.15X l0- eru when the J3 perturbations were applied. The corresponding J3 perturbations applied to the velocities resulted in im- provement from 2.31 X 10-8 eru/sec to 0.25X 10-8 eru/sec.