One of the recurring topics in L. Drewnowski's research was barrelledness of spaces $\ell_\infty(S,\mathcal{A})$ of bounded $\mathcal{A}$-simple scalar-valued functions on a set $S$, where $\mathcal{A}$ is a ring of subsets of $S$. In this talk we will first recall several of his already classical results for $\mathcal{A}$ being an ideal on $S=\mathbb{N}$ and then present new ones, obtained recently by the speaker. We will in particular answer an old question of Drewnowski, Florencio, and Paul concerning so-called local-to-global boundedness properties of ideals as well as analyse and extend Alon-Drewnowski-Luczak's construction of a generalised density ideal on $\mathbb{N}$ induced by a sequence of hypergraphs and not being non-atomic.