Some new quantization conditions for the energy levels of a rigid diatomic dipole molecule in a homogeneous electric field of arbitrary strength, obtained by means of a phase-integral method involving phase-integral approximations of arbitrary order generated from two particular choices of the base function, are expressed in terms of complete elliptic integrals in the first, third and fifth order of the phase-integral approximation. One choice of the base function is especially useful for large absolute values of the magnetic quantum number m. The case m = 0 is considered with another choice of the base function, expected to be useful for small values of $|$m$|$. The great accuracy of the energy levels, yielded by the quantization conditions, is demonstrated for arbitrary electric fields in a number of diagrams pertaining to different values of the quantum numbers. For very weak and very strong electric fields explicit series expansions for the energy levels can be obtained from the quantization conditions, and these expansions are compared with previously obtained series expansions. The investigation confirms that the phase-integral quantization conditions yield very accurate eigenvalues for all values of the electric field strength.