Nucleation rate constants, over a range of deposition potentials, are obtained for the electrocrystallisation of nickel onto a vitreous carbon electrode using the pre-pulse method. This method is based on the analysis of the early stages of two transients, one obtained as a result of the application of a single potential step, and the other resulting from the application of two potential steps (the first as a pre-pulse potential of large amplitude and short duration followed by another at which the nucleation rate is to be determined). A'-values thus obtained are compared with those estimated from the fit of the transients (each recorded at a single potential step at which A' is to be determined) to the generalised equation derived for the model of growth of right-circular cones. The values obtained by the two methods are shown to differ from one another by about a factor of 20. Though it has been possible to obtain with the application of two potential steps, transients which display, in the early stages of deposition, a rising current proportional to the square of the deposition time, it is shown to be impossible to describe adequately the behaviour of these transients in terms of instantaneous formation and subsequent growth of centres for the case of the deposition of nickel onto a vitreous carbon electrode. In the light of the above findings the suitability of the pre-pulse method as a means of estimating A' has therefore been questioned in this example of electrocrystallisation. It has been shown that, even for electrocrystallisation processes where the pre-pulse method is a valid method of estimating A', this method is, strictly speaking, applicable only to the deposition processes obtained at the lower range of potentials (at which A' is 20 times less than the product of the radial growth rate and the square root of the density of nucleation sites). The inability of classical and atomistic theories of nucleation to arrive at plausible values for critical nucleation size has once again been demonstrated.