Abstract Use is made of elementary analytical and experimental results to predict an increased directivity from sources radiating inside or outside plasma layers. It is found that the directivity enhancement is higher when the source is between two plasma layers. Since a single layer, employed as a reflector, gives only a moderate directivity we postulate a double-peaked ionosphere with sources between the two “layers” to explain the large bursts from planets, such as the decametric radiation from Jupiter. For greater directivity, at a given signal frequency, the outside layer of the ionosphere must be near resonance and the inside layer overdense. If the layer near the plasma frequency is viewed as a partially reflecting screen then the maximum power gain for a source between the two layers may be written, approx., G = A (1 + p )/(1 − p ) → ∞ as p → 1, where p is the magnitude of the reflection coefficient of the outside layer and A a constant. For the inside layer p = 1. This analysis predicts radio bursts from other suitable planets or extrasolar bodies and an enhanced radar return from the night E layers on Earth. If now the two postulated spherical layers are non-concentric a longitude dependence of layer separations and, consequently, of resonant frequencies will appear (this assumes constant electron density). Thus the planetary rotation, on this model, gives rise to dynamic spectra of the observed form, i.e., in the “Early” sources the drift is form low to high frequencies, for “Late” sources the reverse is true. In the idealized twin plasma layer model considered neither the plasma losses due to collisions nor the anisotropy of the medium are taken into account.