We present the design of the Oxford SWIFT integral field spectrograph, a dedicated I and z band instrument (0.65μm micron - 1.0μm micron at R~4000), designed to be used in conjunction with the Palomar laser guide star adaptive optics system (PALAO, and its planned upgrade PALM-3000). It builds on two recent developments (i) the improved ability of second generation adaptive optics systems to correct for atmospheric turbulence at wavelengths less than or equal to 1μm micron, and (ii) the availability of CCD array detectors with high quantum efficiency at very red wavelengths (close to the silicon band edge). Combining these with a state-of-the-art integral field unit design using an all-glass image slicer, SWIFT's design provides very high throughput and low scattered light. SWIFT simultaneously provides spectra of ~4000 spatial elements, arranged in a rectangular field-of-view of 44 × 89 pixels. It has three on-the-fly selectable pixel scales of 0.24", 0.16" and 0.08'. First light is expected in spring 2008.