  Only two-body [${\rm F}_{i} \cdot {\rm F}_{j}$] confining potentials have
been considered, thus far, in the quark model without gluons, which by
construction can only depend on the quadratic Casimir operator of the colour
SU(3) group. A three-quark potential that depends on the cubic Casimir operator
is added to the quark model. This results in improved properties of $q^3$
colour non-singlet states, which can now be arranged to have (arbitrarily)
higher energy than the singlet, and the "colour dissolution/anticonfinement"
problem of the ${\rm F}_{i} \cdot {\rm F}_{j}$ model is avoided.
