  We study numerically the coordinate wave functions and the Wigner functions
of the coherent phase states (CPS), paying the main attention to their
differences from the standard (Klauder--Glauber--Sudarshan) coherent states,
especially in the case of high mean values of the number operator. In this
case, the CPS can possess a strong coordinate (or momentum) squeezing, which
is, roughly, twice weaker than for the vacuum squeezed states. The
Robertson--Schr\"odinger invariant uncertainty product in the CPS
logarithmically increases with the mean value of the number operator (whereas
it is constant for the standard coherent states). Some measures of
(non)Gaussianity of CPS are considered.
