We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons cannot outperform classical sorting algorithms by more than a constant factor in time complexity, this is wrong in a space bounded setting. We observe that for all storage bounds n log n>S>log^3 n one can devise a quantum algorithm that sorts n numbers (using comparisons only) in time T=O(n^{3/2} log^{3/2} n / sqrt S). We then show the following lower bound on the time-space tradeoff for sorting n numbers from a polynomial size range in a general sorting algorithm (not necessarily based on comparisons): TS=Omega(n^{3/2}). Hence for small values of S the upper bound is almost tight. Classically the time-space tradeoff for sorting is TS=Theta(n^2).