The instability of drift waves against zonal flows and streamers is discussed. Unlike in previous treatments, we do not make the assumption that their frequency is resonant with driftwave packets. In this more general treatment we find at least two unstable roots even in the simple case of a monochromatic pump drift wave, and potentially an infinite multitude of roots for a more complicated drift wave spectrum. One of them is the well known modulational instability in resonance with the drift wave packets; the other is a new instability corresponding to the inelastic refraction of drift waves at the streamer. It is nontrivial which of the many roots is the most unstable one.