  Let $A$ be the fiber product $R\times_TB$, where $B\to T$ is a surjective
ring homomorphism with regular kernel and $R\subseteq T$ is a ring extension
where $T$ is an overring of $R$. In this paper we provide a characterization of
when $A$ has distinguished Pr\"ufer-like properties and new constructions of
Pr\"ufer rings with zero-divisors. Furthermore we give examples of homomorphic
images of Pr\"ufer rings that are Pr\"ufer without assuming that the kernel of
the surjection is regular. Finally we provide some remarks on the ideal theory
of pre-Pr\"ufer rings.
