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We examine the effect of weak, small-scale magnetic field structure on the rate of reconnection in a strongly magnetized plasma. This affects the rate of reconnection by reducing the transverse scale for reconnection flows and by allowing many independent flux reconnection events to occur simultaneously. Allowing only for the first effect and using Goldreich & Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we find a lower limit for the reconnection speed∼ V ℛ ℳ , where V is the Alfvén speed, ℛ is the Lundquist number, and ℳ is the large-scale magnetic Mach number of the turbulence. We derive an upper limit of∼ V ℳ by invoking both effects. We argue that generic reconnection in turbulent plasmas will normally occur at close to this upper limit. The fraction of magnetic energy that goes directly into electron heating scales as ℛ ℳ , and the thickness of the current sheet …