MPW1K density functional calculations, carried out with the 6-31 +G(d,p) basis set, have been combined with canonical variational transition state theory (CVT) and small-curvature tunneling (SCT) corrections in order to compute the primary kinetic isotope effects for rearrangement of 5-methyl-1,3cyclopentadiene (1) to 1-methyl-1,3-cyclopentadiene (2). The Swain-Schaad exponents, SSE=In(k(H)/k(T))/ In(k(D)/k(T)), for this reaction have been computed over the temperature range 100 - 600 K. Tunneling results in both large positive and large negative deviations from the value of SSE=3.26, expected from consideration of only the effect of the isotopic mass on passage over the reaction barrier. In the rearrangement of 1 to 2, SSE approximate to 3.26, not only at temperatures > 400 K, where tunneling is relatively unimportant, but also around 170 K, where tunneling by both H and D is the dominant mode of reaction. Thus, from an experimental finding that SSE approximate to 3.26 at a single temperature, it cannot be rigorously concluded that tunneling is unimportant. Measurement of SSEs over a broad temperature range is advisable; but measurement of the temperature dependence of just k(H)/k(D) can be used to establish more unequivocally whether tunneling is important, without the necessity of measuring k(T).