Roy and Virendra Singh showed that the harmonic oscillator possesses an infinite string of exact shape-preserving coherent wave-packet states \ensuremath{\Vert}n,\ensuremath{\alpha}〉 having classical motion. In this paper it is shown that the states \ensuremath{\Vert}n,\ensuremath{\alpha}〉 could be obtained from the coherent state \ensuremath{\Vert}\ensuremath{\alpha}〉 and it is also shown how a coherent state \ensuremath{\Vert}\ensuremath{\alpha}〉 could be expanded in the basis of \ensuremath{\Vert}n,\ensuremath{\alpha}〉's. Further, the possibility of ``squeezing'' the state \ensuremath{\Vert}n〉 is investigated and the ``generalized squeezed coherent states'' are obtained. The squeezed coherent states for the displaced oscillator are also defined. The physical meaning of squeezing is also pointed out.