  We introduce a method to construct large classes of MSF wavelets of the Hardy
space H^2(\R) and symmetric MSF wavelets of L^2(\R), and discuss the
classification of such sets. As application, we show that there are uncountably
many wavelet sets of L^2(\R) and H^2(\R). We also enumerate all symmetric
wavelets of L^2(\R) with at most three intervals in the positive axis as well
as 3-interval wavelet sets of H^2(\R). Finally, we construct families of MSF
wavelets of L^2(\R) whose Fourier transform does not vanish in any
neighbourhood of the origin.
