In this paper, we present results and experiments with several methods for bundle adjustment, producing the fastest bundle adjuster ever published in terms of computation and convergence. From a computational perspective, the fastest methods naturally handle the block-sparse pattern that arises in a reduced camera system. Adapting to the naturally arising block-sparsity allows the use of BLAS3, efficient memory handling, fast variable ordering, and customized sparse solving, all simultaneously. We present two methods; one uses exact minimum degree ordering and block-based LDL solving and the other uses block-based preconditioned conjugate gradients. Both methods are performed on the reduced camera system. We show experimentally that the adaptation to the natural block sparsity allows both of these methods to perform better than previous methods. Further improvements in convergence speed are achieved by the novel use of embedded point iterations. Embedded point iterations take place inside each camera update step, yielding a greater cost decrease from each camera update step and, consequently, a lower minimum. This is especially true for points projecting far out on the flatter region of the robustifier. Intensive analyses from various angles demonstrate the improved performance of the presented bundler.