We propose and study a new kind of superposition states: even- and odd
-displaced squeezed states, defined as [D(z) + D(-z)]S(r)\0> and [D(z)
-D(-z)]S(r)\0>, which are characteristic of possessing even and odd ph
oton numbers respectively. We find that the even-displaced squeezed st
ate may exhibit stronger squeezing than that of the ordinary squeezed
state D(z)S(r)\0>.