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Recently we have shown that the reduction of the Carruthers-Nieto symmetricquantum phase fluctuation parameter (U) with respect to its coherent statevalue corresponds to an antibunched state, but the converse is not true.Consequently reduction of U is a stronger criterion of nonclassicality than thelowest order antibunching. Here we have studied the possibilities of reductionof $U$ in intermediate states by using the Barnett Pegg formalism. We haveshown that the reduction of phase fluctuation parameter U can be seen indifferent intermediate states, such as binomial state, generalized binomialstate, hypergeometric state, negative binomial state, and photon added coherentstate. It is also shown that the depth of nonclassicality can be controlled byvarious parameters related to intermediate states. Further, we have providedspecific examples of antibunched states, for which $U$ is greater than itspoissonian state value.

Reduction of Quantum Phase Fluctuations in Intermediate States