Desorption of cesium atoms from a rhenium point emitter in an electric field has been studied by method of field-desorption microscopy (FDM). Dependence of the desorbing field on degree of emitter surface coverage with Cs atoms is established. The heat of Cs-atom adsorption, which is dependent on the surface concentration of adsorbate and work function of the surface, is estimated in the framework of the model of mirror-image forces for field-induced desorption. Saturation of the rhenium emitter with carbon leads to changes in the character of desorption and in the distribution of desorption zones on the emitter surface.