In contrast to most of the existing theory of adaptive finite element methods (AFEM), we design an AFEM for -Δ u = f with right hand side f in H -1 instead of L2. This has two important consequences. First we formulate our AFEM in the natural space for f, which is nonlocal. Second, we show that decay rates for the data estimator are dominated by those for the solution u in the energy norm. This allows us to conclude that the performance of AFEM is solely dictated by the approximation class of u. This is joint work with A. Cohen and R. DeVore.