We investigate a class of phase-like states \ nu; epsilon > with an integer
parameter nu = 0, 1.... which contains the coherent phase states \ epsilon
> as the special case nu = 0. Many characteristics, such as the number sta
tistics and the Susskind-Glogower phase distribution, can be calculated in
a closed way and are discussed. The parameter nu can be continuously interp
olated and extended to a real parameter up to arbitrary nu > -1. Problems o
f the definition of phase variances are discussed. The class of states is c
ompared with the so-called 'phase-optimized' states and it is found that th
e case nu = 2 of them is near to these states. The properties of the consid
ered class of states \ nu; epsilon > provide additional arguments to consid
er the coherent phase states corresponding to nu = 0 as the genuine phase-o
ptimized states. Since the Lommel polynomials play a role in the Fock-state
representation of 'phase-optimized' states as is shown and to prevent misi
nterpretation, it is proposed to rename these states 'Lommel states'. In th
e limiting case of high mean number, they make the transition to Chebyshev
states of second kind and are near to the case nu = 1 of the class of phase
-like states \ nu; epsilon >. The mathematical tools connected with a gener
alization of the geometric series are given in an appendix.