  Canonical instanton theory is known to overestimate the rate constant close
to a system-dependent crossover temperature and is inapplicable above that
temperature. We compare the accuracy of the reaction rate constants calculated
using recent semi-classical rate expressions to those from canonical instanton
theory. We show that rate constants calculated purely from solving the
stability matrix for the action in degrees of freedom orthogonal to the
instanton path is not applicable at arbitrarily low temperatures and employ two
methods to overcome this. Furthermore, as a by-product of the developed
methods, we derive a simple correction to canonical instanton theory that can
alleviate this known overestimation of rate constants close to the crossover
temperature. The combined methods accurately reproduce the rate constants of
the canonical theory along the whole temperature range without the spurious
overestimation near the crossover temperature. We calculate and compare rate
constants on three different reactions: H in the M\"uller--Brown potential,
methylhydroxycarbene $\to$ acetaldehyde and H$_2$ + OH $\to$ H + H$_2$O.
