The Near-Infrared Spectrograph (NIRSpec) is one of the four science instruments of the James Webb Space Telescope. Its focal plane consists of two HAWAII-2RG sensors operating in the wavelength range of 0.6 to 5.0 µm and, as part of characterizing NIRSpec, the noise properties of these detectors under dark and illuminated conditions were studied. Under dark conditions, and as already known, 1/f noise in the detector system causes somewhat higher noise levels than can be accounted for by a simple model that includes white read noise and shot noise on integrated charge. More surprisingly, for high levels of accumulated charge, significantly lower total noise than expected was observed. This effect is shown to be due to pixel-to-pixel correlations introduced by signal-dependent interpixel crosstalk, with an interpixel coupling factor, α , that ranges from ∼0.01 for zero signal to ∼0.03 close to saturation.