  We provide a simple algebraic construction of the twistor spaces of arbitrary
Joyce's self-dual metrics on the 4-manifold H^2 x T^2 that extend smoothly to
nCP^2, the connected sum of complex projective planes. Indeed, we explicitly
realize projective models of the twistor spaces of arbitrary Joyce metrics on
nCP^2 in a CP^4-bundle over CP^1, and show that they contain the twistor spaces
of H^2 x T^2 as dense non-Zariski open subsets. In particular, we see that the
last non-compact twistor spaces can be realized in rank-4 vector bundles over
CP^1 by quite simple defining equations.
