  We study projective Type II degenerations of K3 surfaces polarised by a
certain rank 18 lattice, where the central fibre consists of a pair of rational
surfaces glued along a smooth elliptic curve. Given such a degeneration, one
may construct other degenerations of the same kind by flopping curves on the
central fibre, but the degenerations obtained from this process are not usually
projective. We construct a series of examples which are all projective and
which are all related by flopping single curves from one component of the
central fibre to the other. The components of the central fibres obtained
include weak del Pezzo surfaces of all possible degrees. This shows that
projectivity need not impose any meaningful constraints on the surfaces that
can arise as components in Type II degenerations.
