A dilute polymer solution is modeled as a suspension of noninteracting Hookean dumbbells, and the effect of excluded volume is taken into account by incorporating a narrow Gaussian repulsive potential between the beads of each dumbbell. The narrow Gaussian potential is a means of regularizing a δ-function potential: it tends to the δ-function potential in the limit of the width parameter μ going to zero. Exact predictions of viscometric functions in simple shear flow are obtained with the help of a retarded motion expansion and by Brownian dynamics simulations. It is shown that for relatively small nonzero values of μ, the presence of excluded volume causes a swelling of the dumbbell at equilibrium and shear thinning in simple shear flow. On the other hand, a δ-function excluded-volume potential does not lead to either swelling or to shear thinning. Approximate viscometric functions, obtained by assuming that the bead-connector vector is described by a Gaussian nonequilibrium distribution function, are found to be accurate above a threshold value of μ, for a given value of the strength of excluded-volume interaction, z. A first-order perturbation expansion reveals that the Gaussian approximation is exact to first order in z. The predictions of an alternative quadratic excluded-volume potential suggested earlier by Fixman (J. Chem. Phys. 1966, 45, 785, 793) are also compared with those of the narrow Gaussian potential.