Near-infrared array detectors, like the James Webb Space Telescope (JWST) NIRSpec’s Teledyne’s H2RGs, often provide reference pixels and a reference output. These are used to remove correlated noise. Improved reference sampling and subtraction (IRS²) is a statistical technique for using this reference information optimally in a least-squares sense. Compared with the traditional H2RG readout, IRS² uses a different clocking pattern to interleave many more reference pixels into the data than is otherwise possible. Compared with standard reference correction techniques, IRS² subtracts the reference pixels and reference output using a statistically optimized set of frequency-dependent weights. The benefits include somewhat lower noise variance and much less obvious correlated noise. NIRSpec’s IRS² images are cosmetically clean, with less 1/f banding than in traditional data from the same system. This article describes the IRS² clocking pattern and presents the equations needed to use IRS² in systems other than NIRSpec. For NIRSpec, applying these equations is already an option in the calibration pipeline. As an aid to instrument builders, we provide our prototype IRS² calibration software and sample JWST NIRSpec data. The same techniques are applicable to other detector systems, including those based on Teledyne’s H4RG arrays. The H4RG’s interleaved reference pixel readout mode is effectively one IRS² pattern.