The least-action semiclassical algorithm for multidimensional tunneling probabilities [B. C. Garrett and D. G. Truhlar, J. Chem. Phys. 79, 4931 (1983)] has usually been employed by interpolating tunneling paths between two limits, a least-motion limit appropriate for large reaction-path curvature and a minimum-energy limit appropriate for small reaction-path curvature. In the present study we test whether, when the reaction-path curvature is small, more accurate results might be obtained by using a general small-curvature reference path. Least-action algorithms with both types of reference paths are compared to each other, to five other semiclassical approximations, and to accurate quantal dynamical rate constants for one three-dimensional and two collinear reactions with the mass combination ℒ + ℋ ℒ′ → ℒ ℋ + ℒ′ where ℒ and ℋ′ denote light atoms (H or D) and ℋ denotes a heavy atom (Br). We find, perhaps surprisingly, that the usual least-action method works best. This is encouraging because the minimum-energy reference is easier than the small-curvature reference to extend to polyatomic reactions.