The 2q-th pseudomoment Ψ2q,α(x) of the α-th power of the Riemann zeta function is defined to be the 2q-th moment of the partial sum up to x of ζ α on the critical line. Using probabilistic methods of Harper, we prove upper and lower bounds for these pseudomoments when q ≤ 1 2 and α ≥ 1. Combined with results of Bondarenko, Heap and Seip, these bounds determine the size of all pseudomoments with q > 0 and α ≥ 1 up to powers of log log x, where x is the length of the partial sum, and it turns out that there are three different ranges with different growth behaviours. In particular, the results give the order of magnitude of Ψ2q,1(x) for all q > 0.