Are there any flags that could be used to alter (i.e. improve) the convergence rate

We are experiencing slow convergence in that 216, 432 and then 864 Fourier modes' results are still changing slightly. 1728 modes would not run in a practical amount of time. Are there any ways to improve the convergence rate? I read in Liu and Fan's 2011 paper that there have been formulation edits that impact convergence, but I'm not clear if those are in place or if one has to invoke them via a flag, etc. Thanks.