Numerical optimization is used to construct new orthonormal compactlysupported wavelets with Sobolev regularity exponent as high as possible amongthose mother wavelets with a fixed support length and a fixed number ofvanishing moments. The increased regularity is obtained by optimizing thelocations of the roots the scaling filter has on the interval (pi/2,\pi). Theresults improve those obtained by I. Daubechies [Comm. Pure Appl. Math. 41(1988), 909-996], H. Volkmer [SIAM J. Math. Anal. 26 (1995), 1075-1087], and P.G. Lemarie-Rieusset and E. Zahrouni [Appl. Comput. Harmon. Anal. 5 (1998),92-105].
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