  A class of states of the electromagnetic field involving superpositions of
all the excited states above a specified low energy eigenstate of the
electromagnetic field is introduced. These states and the photon-added coherent
states are shown to be the limiting cases of a generalized photon-added
coherent states. This new class of states is nonclassical, non-Gaussian and has
equal uncertainties in the field quadratures. For suitable choices of
parameters, these uncertainties are very close to those of the coherent states.
Nevertheless, these states exhibit sub-Poissonian photon number distribution,
which is a nonclassical feature. Under suitable approximations, these states
become the generalized Bernoulli states of the field. Nonclassicality of these
states is quantified using their entanglement potential.
