A value of 0. 0283 ± 0. 0008 was obtained for the K- shell internal conversion coefficient, a_K, of the 344-kev, E2 transition in Gd¹⁵² using an electron-electron coincidence method. This value is relative to a value of 1.135 ± 0. 010 for the total internal conversion coefficient, a, of the 122-kev, E2 transition in Sm¹⁵² . a_.K/a ratios of 0. 786 ± 0. 004 and 0. 589 ± 0. 003 were measured for the 344- and 122-kev transitions, respectively. The apparent 9% discrepancy with theory for a_K of the 344-kev transition is not explained. The result is in excellent agreement with another measurement and also in agreement with an apparent lower trend for a_K's of E2 transitions in near spherical nuclei. The a_K value for the 122-kev transition is in good agreement with theory. Additional measurements were performed on the 123- and 87-kev, E2 transitions in Gd¹⁵⁴ and Dy¹⁶⁰, respectively, and a_K/a ratios of 0. 531 ± 0. 007 and 0. 341 ± 0. 011 were obtained. Construction and performance of the beta-ray spectrometers used in these coincidence measurements are described along with limitations of the experimental technique.