Analytic design criteria are provided to determine if a digital magnetic recording system can overwrite under worst-case conditions. The worst-case condition is taken to be a bubble of reversed magnetization in an otherwise saturated medium, written by applying current to a stationary recording head. A leading and a trailing transition are formed, creating a large demagnetizing field opposing the head field. Although the leading transition is commonly thought to be unimportant in saturation writing, its demagnetizing field can significantly hamper the writing of the trailing transition. First, self-consistent numerical calculation shows the characteristics of the bubble and its associated fields. Then the bubble is approximated analytically by a biquadratic form, and the demagnetizing field at the bubble center is compared with the field necessary to saturate the medium. A rapid loss of overwrite ability with decreasing gap-length is demonstrated. The importance of including image fields for thin-film heads is discussed. Graphical representations are given for the minimum gap-length necessary for overwrite. A relation between media parameters, bit density, and magnetic energy/bit in commercial disk drives is discussed.