This paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems. Comparing with the existing relevant literature, the systems under investigation allow more serious unknowns/uncertainties. More importantly, by remarkably reducing the dimension of dynamic compensator for system unknowns (from n to 2) and considerably diminishing the overparametrisation in the existing literature, this paper proposes an improved design scheme for adaptive state-feedback controllers. It is turned out that, with the designed controller in loop, all the closed-loop system states are globally bounded and the original system states converge to the origin, both in the sense of probability one. A simulation example is also given to demonstrate the effectiveness of the theoretical results.