We show that the sQ-degree of a hypersimple set includes an infinite collection of $$sQ_1$$ -degrees linearly ordered under $$\le _{sQ_1}$$ with order type of the integers and each c.e. set in these sQ-degrees is a hypersimple set. Also, we prove that there exist two c.e. sets having no least upper bound on the $$sQ_1$$ -reducibility ordering. We show that the c.e. $$sQ_1$$ -degrees are not dense and if a is a c.e. $$sQ_1$$ -degree such that $$o_{sQ_1}<_{sQ_1}a<_{sQ_1}o'_{sQ_1}$$, then there exist (...) infinitely many pairwise sQ-incomputable c.e. sQ-degrees $$\{c_i\}_{i\in \omega }$$ such that $$(\forall \,i)\;(a<_{sQ_1}c_i<_{sQ_1}o'_{sQ_1})$$. (shrink)