The effect of air drag on satellite orbits of small eccentricity, 0.01 $\lesssim$ e $\lesssim$ 0.2, is considered. A model of the atmosphere that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation, is adopted. The equation governing the changes due to drag in the argument of perigee $\omega$, during one revolution of the satellite, is integrated with the assumption that the density scale height H is constant. The resulting expression for $e\Delta \omega$ is presented to third order in e. Compact expressions for $e\Delta \omega$ and $e\Delta \omega/\Delta T_D$, where $\Delta T_D$ is the corresponding change in the period, are obtained when H is allowed to vary with altitude. It is shown that there is an equivalence between the variable-H and the constant-H equations, provided that the value of H used in the latter is chosen appropriately.