The generation of half-odd harmonic emissions by shell-like electron distribution functions as recently observed by ISEE 1 is considered. The investigation includes (a) the analysis of the type of observed distributions and their representation by equivalent simplified forms consisting of a 'shell' in velocity space and a cold background at rest, (b) the possible generation by such distribution functions of almost perpendicular electrostatic emissions of half-odd harmonics of the electron gyrofrequency, and (c) the possible enhancement of one (or more) particular emissions lines. We show that in a first approximation, neglecting temperature effects, a distribution of the type observed by ISEE 1 can be considered to be made up of an infinite number of mnoenergetic beams characterized by different pitch angles and a cold background at rest. If these beams are considered in pairs, it is found that they support unstable electrostatic waves resulting from the resonant coupling of plasma (Cerenkov) modes and cyclotron modes; these waves occur at about odd, half-harmonics of the electron gyrofrequency. The maximum growth rates caused by the interaction of the two-electron beams may be strongly affected by the presence of a third, cold-background component: under certain circumstances, a particular mode (at a given frequency, &ohgr; = (m+1/2)&OHgr;,m = 1,2,...) can be enhanced in relation to the neighboring modes, thus dominating the discrete wave spectrum.