In radio interferometry imaging, the gridding procedure of convolving visibilities with a chosen gridding function is necessary to transform visibility values into uniformly sampled grid points. We propose here a parameterised family of least-misfit gridding functions which minimise an upper bound on the difference between the DFT and FFT dirty images for a given gridding support width and image cropping ratio. When compared with the widely used spheroidal function with similar parameters, these provide more than 100 times better alias suppression and RMS misfit reduction over the usable dirty map. We discuss how appropriate parameter selection and tabulation of these functions allow for a balance between accuracy, computational cost and storage size. Although it is possible to reduce the errors introduced in the gridding or degridding process to the level of machine precision, accuracy comparable to that achieved by CASA requires only a lookup table with 300 entries and a support width of 3, allowing for a greatly reduced computation cost for a given performance.
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