Object: Modern computational MRI denoising approaches are often designed assuming fixed k-space coverage. This contrasts with earlier acquisition-design literature that leveraged k-space coverage modifications (e.g., reducing spatial resolution) to improve SNR. This work investigates whether the performance of modern computational denoising methods can be further enhanced by k-space coverage modifications. Materials and Methods: Using realistic simulations of noisy data, k-space coverage and averaging patterns were optimized for two advanced image denoising/reconstruction approaches: parallel imaging with total variation regularization and a U-Net neural network. For reference, comparisons against classical linear filtering/apodization methods were also performed. Performance was quantified using normalized root-mean-squared error (NRMSE) and structural similarity (SSIM) metrics. Results: Advanced computational denoising methods can be substantially enhanced, both quantitatively and qualitatively, by reducing the spatial resolution of the acquisition to improve SNR. Indeed, even simple linear filtering/apodization with optimized k-space coverage can rival advanced methods using naive higher-resolution coverage. Discussion: Classical acquisition design principles that allow spatial resolution to be traded for SNR enhancement are still very relevant for modern computational denoising techniques. However, the optimization of k-space coverage and denoising/reconstruction methods can also be somewhat confounded because the NRMSE and SSIM metrics have low sensitivity to spatial resolution.