Post-annealing studies in different atmospheres combined with high resolution x-ray studies on epitaxial ZnO and Zn1-xCoxO films revealed that the c-axis lattice parameter decreases when interstitial zinc is removed from ZnO. The 'c' parameter change reverses sign when samples are re-annealed in a Zn-rich atmosphere. Stronger ferromagnetism occurs in Zn1-xCoxO film for higher 'c' parameters and hence higher Zn interstitial concentrations.