Near the deconfinement transition of SU(2) gauge theory the finite-size scaling behaviour of the order parameter, the susceptibility and the normalized fourth cumulant g(r) is studied on N(simga)3 x N(tau) lattices with N(tau) = 4 and 6 and N(sigma) = 8, 12, 18, 24 or 26. For that purpose we have calculated new high-statistics data for N(tau) = 6 and re-evaluated previous results obtained for N(tau) = 4. In both cases we used the density of states method. We determine the critical coupling and with a new way of phenomenological renormalization the critical exponents. For N(tau) = 6 we find that 4/g(c, infinity)2 = 2.4265(3). Using the results for the critical temperature obtained for different N(tau) we examine the approach to asymptotic scaling.