  It is shown that there exists a twistor space on the $n$-fold connected sum
of complex projective planes $n\mathbb{CP}^2$, whose algebraic dimension is one
and whose general fiber of the algebraic reduction is birational to an elliptic
ruled surface or a K3 surface. The former kind of twistor spaces are
constructed over $n\mathbb{CP}^2$ for any $n\ge 5$, while the latter kind of
example is constructed over $5\mathbb{CP}^2$. Both of these seem to be the
first such example on $n\mathbb{CP}^2$. The algebraic reduction in these
examples is induced by the anti-canonical system of the twistor spaces. It is
also shown that the former kind of twistor spaces contain a pair of non-normal
Hopf surfaces.
