The energy eigenvalue expression for a diatomic vib-rotor with the simple Kratzer potential De[(r - re)/r]2 {xmathmode}approximates poorly most of the anharmonic and rotation-vibration interaction terms, as shown by its expansion in a Dunham-type series and comparison with experimentally determined Dunham Yij coefficients. To correct this behavior, the expression was modified by terms dependent on the vibrational and rotational quantum numbers built directly into the formula. The formula thus modified turns out to be a useful alternative to the Dunham expansion for not-too-long progressions or sequences of rovibrational bands as it provides a precision of fit better or at least comparable to the Dunham series with the same number of adjustable parameters. Application of this modified energy expression to individual bands (such as fundamental bands) is shown to yield accurate estimates for equilibrium rotational constants Be and equilibrium internuclear distances re which are in many cases better than values obtained from standard power series analyses of single bands. Useful estimates are also obtained for the zero-order vibrational frequencies omegae and for the positions of the lower overtone or combination bands. Such information is otherwise not accessible from a conventional analysis of an individual band. Copyright 1999 Academic Press.