  We study the well-known Vertex Cover problem parameterized above and below
tight bounds. We show that two of the parameterizations (both were suggested by
Mahajan, Raman and Sikdar, J. Computer and System Sciences, 75(2):137--153,
2009) are fixed-parameter tractable and two other parameterizations are
W[1]-hard (one of them is, in fact, W[2]-hard).
