The d-c.e. (difference of c.e.) and dbc (divergence bounded computable) reals are two important subclasses of Δ_2~0-reals which have very interesting computability-theoretical as well as very nice analytical properties. Recently, Downey, Wu and Zheng have shown by a double witness technique that not every Δ_2~0-Turing degree contains a d-c.e. real. In this paper we show that the classes of Turing degrees of d-c.e., dbc and Δ_2~0 reals are all different.
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