  Solvable Hamiltonians for the $\beta$ and $\gamma$ intrinsic shape
coordinates are proposed. The eigenfunctions of the $\gamma$ Hamiltonian are
spheroidal periodic functions, while the Hamiltonian for the $\beta$ degree of
freedom involves the Davidson's potential and admits eigenfunctions which can
be expressed in terms of the generalized Legendre polynomials. The proposed
model goes to X(5) in the limit of $|\gamma|$-small. Some drawbacks of the X(5)
model, as are the eigenfunction periodicity and the $\gamma$ Hamiltonian
hermiticity, are absent in the present approach. Results of numerical
applications to $^{150}$Nd, $^{154}$Gd and $^{192}$Os are in good agreement to
the experimental data. Comparison with X(5) calculations suggests that the
present approach provides a quantitative better description of the data. This
is especially true for the excitation energies in the gamma band.
