The stochastic implicit Euler scheme and its variants can be used to prevent non-physical behaviour that may emerge when coupling Monte Carlo neutron transport and isotopic depletion solvers for spatially-decoupled reactor problems. However, stochastic implicit methods tend to require many iterations to obtain a stable solution. This paper demonstrates that this is due to using a sub-optimal relaxation scheme: rather than using a variable relaxation factor, a fixed relaxation factor can give a more stable solution in fewer iterations. Furthermore, like stochastic implicit schemes, even though multiple transport solutions are required, using a fixed relaxation factor allows computational effort to be reduced by lowering the number of particles simulated during the corrector step while still providing stable results. This shows that using a fixed relaxation factor to stabilise Monte Carlo burn-up calculations can be more effective than applying the stochastic approximation.