overlapping labels

Good evening,
 
I am trying to add labels to the point of a simple plot, using the
text() function; the problem is that sometimes, if two points are too
close to each other, labels overlap and are no longer readable.
I was wondering whether there are options that I can use to prevent this
overlapping (by, for example, placing labels alternatively above and
below the plotted curve), or whether I should use another set of
graphical functions (grid or lattice packages).
Does anybody have suggestions?