An examination of the signs of nuclear quadrupole moments and of the nuclear states which produce them affords fairly striking evidence that a positive quadrupole moment tends to lower the energy of a nuclear state. For nuclei containing several particles outside of closed shells the shell model often does not uniquely specify the sign of the quadrupole moment. The ground states of such nuclei are, however, known to have positive quadrupole moments in the great majority of cases. Additional evidence for this tendency is provided by a discussion of: (a) The ground states of Cu, Ga, As, Br, and Rb. (b) The exceptions to the single-particle version of the shell model, Na23, Mn55, Se79, Eu153, and Yb173. (c) The spins of ground states of odd-odd N=Z nuclei. The favoring of positive quadrupole moments appears to be accounted for by electrostatic and other known forces in conjunction with large core deformations. It may, perhaps, also be influenced by tensor forces.