The “proportionate” family of adaptive filters has been in use over the past decade. Their fast convergence for sparse systems makes them particularly useful in the network echo canceller application. Recently, an iterative form of the proportionate affine projection algorithm (PAPA), derived from the basic principles of basis pursuit, has been shown to have remarkably fast convergence for such sparse systems. The number of samples for convergence is proportional to the sparseness of the system which means that often full convergence occurs in fewer samples than the length of the system's impulse response. Here, we introduce a lower complexity implementation with the same performance that is an iterative version of proportionate normalized least mean squares (PNLMS).