from direct evaluation. In practice, any interferometric observation is likely to be arranged such that the mean value of $w$ is approximately zero. Therefore, there are unlikely to be outlying, small Gaussians that would allow for increasing the box size. Once again, this optimisation has limited impact.

3.  S91 proposes doing direct evaluation for boxes containing only a few evaluation points. As we are evaluating on a regular grid, we have the same number of evaluation points inside each box, so applying this optimisation would degenerate into standard gridding.

4.  S91 proposes a method for avoiding needlessly accurate computation, i.e. for large scales (which are smoother than small ones) more boxes are updated, but smaller number of Taylor coefficients (i.e. the order $q$ described in Section \[sec:gridding\]) per box can be updated. This optimisation *is* useful and derives the most benefit for visibilities with large scales ($|w|$ large, see section \[sec:performance\].). We have incorporated this optimisation in Equation \[eq:qerror\].

5.  S91 notes that the equation to calculate the order (Equation \[eq:qerror\]) overestimates the error by at sometimes two orders of magnitude. Memory bandwidth and operations can be saved by ‘cheating’ on the value of $q$ by decrementing $q$ by some 