We show that the solutions describing charged rotating black holes in five-dimensional-gauged supergravities found recently by Cvetic, Lu and Pope (2004 Charged Kerr-de Sitter black holes in five dimensions Phys. Lett. B 598 273, 2004 Charged rotating black holes in five dimensional U (1)(3) gauged N = 2 supergravity Phys. Rev. D 70 081502) are completely specified by the mass, charges and angular momentum. The additional parameter appearing in these solutions is removed by a coordinate transformation and redefinition of parameters. Thus, the apparent hair in these solutions is unphysical.