An analytical theory of current‐driven, ion‐cyclotron turbulence that treats incoherent phase‐space density granulations (clumps) is presented. In contrast to previous investigations it focuses on the physically relevant regime of weak collective dissipation, where waves and clumps coexist. The threshold current for nonlinear instability is calculated and is found to deviate from the linear threshold by up to 7%. A necessary condition for the existence of stationary wave‐clump turbulence is derived and shown to be analogous to the test‐particle model, fluctuation–dissipation theorem result. The structure of three‐dimensional magnetized clumps is characterized. It is proposed that nonlinear instability is saturated by collective dissipation due to ion‐wave scattering. For this wave‐clump turbulence regime, it is found that the fluctuation level (e&Jgr;/Te)rms≤0.1, and that the modification of anomalous resistivity to levels predicted by conventional nonlinear wave theories is moderate. In marked contrast to the quasilinear prediction, it is also shown that ion heating significantly exceeds electron heating, and that a drag force on electrons sustains a steady current and is set up to counteract the accelerating electric field along field lines.