  Based on the competition between $\gamma$-stable and $\gamma$-rigid
collective motions mediated by a rigidity parameter, a two-parameter exactly
separable version of the Bohr Hamiltonian is proposed. The $\gamma$-stable part
of the Hamiltonian is restricted to stiff oscillations around the $\gamma$
value of the rigid motion. The separated potential for $\beta$ and $\gamma$
shape variables is chosen such that in the lower limit of this parameter, the
model recovers exactly the ES-$X(5)$ model, while in the upper limit it tends
to the prolate $\gamma$-rigid solution $X(3)$. The combined effect of the
rigidity and stiffness parameters on the energy spectrum and wave function is
duly investigated. Numerical results are given for few nuclei showing such
ambiguous behaviour.
