Iterative reconstruction algorithms for non-Cartesian MRI can have slow convergence due to the nonuniform density of k-space samples. Convergence speed can be improved by including the density compensation function into the algorithm, but current techniques for doing so can lead to SNR penalties or algorithm divergence. Here, we combine the use of density compensation with a line search under the MFISTA framework. The method has the convergence guarantees of MFISTA while gaining the speed improvements of using the density compensition function. The algorithm generalizes further to any FISTA algorithm.