The molecular beam electric resonance technique has been used to examine the hyperfine spectrum of (LiI)-Li-7 to determine the nuclear hexadecapole interaction of the iodine nucleus. The nuclear magnetic octupole interaction was also considered but found to be marginally significant. A total of 172 transitions in vibrational states 0-3 and rotational states 1-6 have been included in a fit to determine the iodine nuclear quadrupole, spin- rotation, and hexadecapole interactions, the lithium quadrupole and spin- rotation interactions, and the tensor and scalar parts of the spin- spin interaction. Vibration and rotation dependencies of these constants have been determined. The results include: eHh = -0.0151(30), eQ(I)q(I) = -194351.212(17) - 8279.521(46)(upsilon + 1/2) + 100.616(34) (upsilon + 1/2)(2) - 0.3949(73)(upsilon + 1/2)(3) - 6.41977(50) J(J+1) + 0.10593(33)(upsilon + 1/2) J(J+1), eQ(Li)q(Li) = 172.613(52) - 3.26 (14)(upsilon + 1/2) + 0.00145(87) J(J+1), c(I) = 6.80260(32) + 0.00303(49)(upsilon + 1/2) = 0.000118(13) J(J+1), c(Li) = 0.75872 (72) - 0.0088(11)(upsilon + 1/2), c(3) = 0.62834(68) - 0.0050(11) (upsilon + 1/2), c(4) = 0.06223(36) + 0.00041(26)(upsilon + 1/2), and e Omega(I)omega＇(I) = 0.000112(73), all in kHz with one standard deviation uncertainties for the last 2 digits in ().