  Inspired by Bartoszy\'nski's work on small sets, we introduce a new ideal
defined by interval partitions on natural numbers and summable sequences of
positive reals. Similarly, we present another ideal that relies on
Bartoszy\'nski's and Shelah's characterization of $F_\sigma$ measure zero sets.
We demonstrate that they are $\sigma$-ideals and provide characterizations of
the families of all small sets and the ideal induced by $F_\sigma$ measure zero
sets. We also study the cardinal characteristics associated with the introduced
ideals. We discuss their connection to Cicho\'n's diagram and present related
consistency results.
