Some confusion in the literature is clarified regarding the properties of microstrip-line higher modes in the neighborhood of cutoff. It is shown that those modes become leaky in that range; with the aid of the steepest-descent plane, one finds that the continuous spectrum can be characterized in a highly convergent manner by essentially a single leaky mode. The leakage occurs in two forms: a surface wave and a space wave. For structures without a top cover, it is found that almost all of the leakage is in the form of a space wave, so that an efficient leaky-wave antenna of particularly simple configuration may be designed that consists of just a length of uniform microstrip line fed in its first higher mode. An accurate leaky-wave analysis is developed that explains quantitatively the performance features and the limitations of this class of antennas.