Recent studies of genome-wide nucleosomal organization suggest that the DNA sequence is one of the major determinants of nucleosome positioning. Although the search for underlying patterns encoded in nucleosomal DNA has been going on for about 30 years, our knowledge of these patterns still remains limited. Based on our evaluations of DNA deformation energy, we developed new scoring functions to predict nucleosome positioning. There are three principal differences between our approach and earlier studies: (i) we assume that the length of nucleosomal DNA varies from 146 to 147 bp; (ii) we consider the anisotropic flexibility of pyrimidine-purine (YR) dimeric steps in the context of their neighbors (e.g., YYRR versus RYRY); (iii) we postulate that alternating AT-rich and GC-rich motifs reflect sequence-dependent interactions between histone arginines and DNA in the minor groove. Using these functions, we analyzed 20 nucleosome positions mapped in vitro at single nucleotide resolution (including clones 601, 603, 605, the pGUB plasmid, chicken beta-globin and three 5S rDNA genes). We predicted 15 of the 20 positions with 1-bp precision, and two positions with 2-bp precision. The predicted position of the '601' nucleosome (i.e., the optimum of the computed score) deviates from the experimentally determined unique position by no more than 1 bp - an accuracy exceeding that of earlier predictions. Our analysis reveals a clear heterogeneity of the nucleosomal sequences which can be divided into two groups based on the positioning 'rules' they follow. The sequences of one group are enriched by highly deformable YR/YYRR motifs at the minor-groove bending sites SHL+/- 3.5 and +/- 5.5, which is similar to the alpha-satellite sequence used in most crystallized nucleosomes. Apparently, the positioning of these nucleosomes is determined by the interactions between histones H2A/H2B and the terminal parts of nucleosomal DNA. In the other group (that includes the '601' clone) the same YR/YYRR motifs occur predominantly at the sites SHL +/- 1.5. The interaction between the H3/H4 tetramer and the central part of the nucleosomal DNA is likely to be responsible for the positioning of nucleosomes of this group, and the DNA trajectory in these nucleosomes may differ in detail from the published structures. Thus, from the stereochemical perspective, the in vitro nucleosomes studied here follow either an X-ray-like pattern (with strong deformations in the terminal parts of nucleosomal DNA), or an alternative pattern (with the deformations occurring predominantly in the central part of the nucleosomal DNA). The results presented here may be useful for genome-wide classification of nucleosomes, linking together structural and thermodynamic characteristics of nucleosomes with the underlying DNA sequence patterns guiding their positions.