Coefficients of the odd zonal harmonics in the Earth's gravitational potential— J 3, J 5, J 7, etc.—are evaluated by analysing the variations in orbital eccentricity of 22 satellites, chosen to give the widest and most uniform possible distribution in semi major axis and inclination. These satellites provide 22 simultaneous equations for the coefficients J 3, J 5, etc., and the equations are solved by the least-squares method for sets of coefficients of successively higher order. The solutions show that J 9 may be taken as zero, and that, for 9 < n < 33, the odd J n do not differ significantly from zero unless n is a multiple of 3. Consequently J 11, J 13, J 17, J 19, J 23, J 25, J 29 and J 31 can be taken as zero, and it is feasible to carry the solutions to harmonics of much higher degree than was previously possible. The best representation of the odd zonal harmonics in the geopotential is provided by the following set of values: 10 6 J 3 = −2·54 ± 0·01 10 6 J 5 = −0·21 ± 0·01 10 6 J 7 = −0·40 ± 0·01 10 6 J 15 = −0·20 ± 0·03 10 6 J 21 = 0·26 ± 0·05 10 6 J 27 = −0·15 ± 0·10 J 9 = J 11 = J 13 = J 17 = J 19 = J 23 = J 25 = J 29 = J 31 = 0.