  In this paper we shall consider a couple of properties of $\sigma$-ideals and
study relations between them. Namely we will prove that $\mathfrak{c}$-cc
$\sigma$-ideals are tall and that the Weaker Smital Property implies that every
Borel $\mathcal{I}$-positive set contains a witness for non($\mathcal{I}$) as
well, as satisfying ccc and Fubini Property. We give also a characterization of
nonmeasurability of $\mathcal{I}$-Luzin sets and prove that the ideal
$[\mathbb{R}]^{\leq\omega}$ does not posses the Fubini Property using some
interesting lemma about perfect sets.
