We study the degree structure of bQ-reducibility and we prove that for any noncomputable c.e. incomplete bQdegree a, there exists a nonspeedable bQ-degree incomparable with it. The structure D b s of the bs-degrees is not elementary equivalent neither to the structure of the be-degrees nor to the structure of the e-degrees. If c.e. degrees a and b form a minimal pair in the c.e. bQ-degrees, then a and b form a minimal pair in the bQ-degrees. Also, for every simple set S there is a noncomputable nonspeedable set A which is bQ-incomparable with S and bQ-degrees of S and A does not form a minimal pair.