Stochastic local search algorithms based on the WalkSAT architecture are among the best known methods for solving hard and large instances of the propositional satisfiability problem (SAT). The performance and behaviour of these algorithm critically depends on the setting of the noise parameter, which controls the greediness of the search process. The optimal setting for the noise parameter varies considerably between different types and sizes of problem instances; consequently, considerable manual tuning is typically required to obtain peak performance. In this paper, we characterise the impact of the noise setting on the behaviour of WalkSAT and introduce a simple adaptive noise mechanism for WalkSAT that does not require manual adjustment for different problem instances. We present experimental results indicating that by using this self-tuning noise mechanism, various WalkSAT variants (including WalkSAT/SKC and Novelty+) achieve performance levels close to their peak performance for instance-specific, manually tuned noise settings.