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We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra et al. (1982) towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximate the successive minima of the lattice in nearly the same way as LLL-bases. For integer lattices of dimension n given by a basis of length 2o(n), SLLL-reduction runs in O(n5+ε) bit operations for every ε 0, compared to O(n7+ε) for the original LLL and to O(n6+ε) for the LLL-algorithms (Schnorr, 1988 and Storjohann, 1996). We present an even faster algorithm for SLLL-reduction via iterated subsegments running in O(n3 logn) arithmetic steps. Householder reflections are shown to provide better accuracy than Gram-Schmidt for orthogonalizing LLL-bases in floating point arithmetic.