  One-parameter exactly separable versions of the X(5) and X(5)-beta^2 models,
labelled as ES-X(5) and ES-X(5)-beta^2 respectively, are derived by using in
the Bohr Hamiltonian potentials of the form u(beta)+u(gamma)/beta^2. Unlike
X(5), in these models the beta_1 and gamma_1 bands are treated on equal
footing. Spacings within the gamma_1 band are well reproduced by both models,
while spacings within the beta_1 band are well reproduced only by
ES-X(5)-beta^2, for which several nuclei with R_{4/2}=E(4_1^+)/E(2_1^+) ratios
and [normalized to E(2_1^+)] beta_1 and gamma_1 bandheads corresponding to the
model predictions have been found.
