  Considering the two-dimensional sloshing problem, our main focus is to
construct domains with interior high spots; that is, points, where the free
surface elevation for the fundamental eigenmode attains its critical values.
The so-called semi-inverse procedure is applied for this purpose. The existence
of high spots is proved rigorously for some domains. Many of the constructed
domains have multiple interior high spots and all of them are bulbous at least
on one side.
