Degrees of sets having no subsets of higher m- and tt-degree

We consider sets without subsets of higher $m$- and $tt$-degree, that we call $m$-introimmune and $tt$-introimmune sets respectively. We study how they are distributed in partially ordered degree structures. We show that: egin{itemize} item each computably enumerable weak truth-table degree contains $m$-introimmune $Pi^0_1$-sets; item each hyperimmune degree contains bi-$m$-introimmune sets. end{itemize} Finally, from known results we establish that each degree {f a} with ${f a}'geq {f 0}''$ covers a degree containing $tt$-introimmune sets.