The authors recall the application of fixed-lag particle smoothing (FLPS) to perform blind turbo equalisation under a Bayesian framework, assuming that the noise variance is unknown. This approach has been successfully applied in previous works, at the price of increasing equaliser computational complexity. This study's main contribution is to propose a strategy to monitor, along the iterations, the quality of channel estimate and soft information about the coded symbols, to switch from FLPS to the BCJR algorithm when performing soft-input softoutput equalisation. This approach allows saving significant computational effort without affecting bit error rate performance. Simulation results and a careful computational complexity analysis show the effectiveness of the techniques herein presented.