The Comet Halley nucleus is modeled as a homogeneous, triaxial ellipsoid precessing under the torque of nine randomly placed cometographically fixed jets. We employ the ansatz of random jets to elicit the dominant periods in the solar-heating-induced emission spectrum and to test the permanence of the spin state against disruption by the torque from the jets. The precessing nucleus is followed numerically using nonsingular, matrix differential equations. Eight models in the literature are evaluated in relation to the constraints imposed by: (i) the observed long-axis directions at the spacecraft encounters, (ii) the observed ground-based emission periods harmonically related to ≈7.4 days ( M. J. S. Belton 1990, Icarus 86, 30-51), (iii) the need for a 2-day total spin period in models of the jet morphology, (iv) the limitation on the net rotation (roll) around the long axis between the Vega 2 and Giotto spacecraft encounters ( Smith et al. 1987 , Nature (London) 326, 573-574), (v) the resistance to spin-state change from the torque of the jets, and (vi) the return of the nucleus to the same spatial orientation roughly every 7.4 days. All eight models were constructed to satisfy spacecraft-encounter long-axis directions. The ground-based emission periods disfavor the five models (numbered 1, 2, 6, 7, and 8 below) that were derived from a 2.2-day long-axis precession. The same models fail to repeat their orientation every 7.4 days. The three remaining models (3, 4, and 5 below) proposed by Belton (1990) are based on a 3.7-day long-axis precession and his Assumption SV1G2 that the long axis is reversed at Vega 1 and reflected in the plane of the sky as seen from Giotto. Models 1, 3, and 8 fail the test of a permanent spin state. The extremely inhomogeneous LAM Model 4 satisfies the six constraints. But, the emission spectrum of Model 4 is weighted toward the fifth harmonic of 7.4 days while that of Model 5 is weighted toward the third. Models 1, 2, 5, and 7 require reexamination of the Smith et al (1987 , Nature 326, 573-574) constraint. Models 3 and 5 require reanalysis of the jet morphology with a 3-day spin period.