  This paper is a continuation of work started in \cite{njampavcont} on
preserving continuity in ideal topological spaces. We will deal with
$\theta$-continuity and weak continuity and give their translations in ideal
topological spaces. As consequences of those results, we will prove that every
$\theta$-continuous function is continuous if topologies are generated by
$\theta$-open sets and we will give an example of weakly continuous function
which is not $\tau_\theta$-continuous. This will complete the diagram of
relations between continuous, $\tau_\theta$-continuous, $\theta$-continuous,
weakly continuous and faintly continuous functions.
