The Quad Tree (QT) is a simple but effective image compression method. This paper presents a novel variation of the QT called the Interpolating Leaf Quad Tree (ILQT). The ILQT stores multiple values in each quadrant in order to better approximate the image whilst using less memory. The ILQT is shown to outperform JPEG-2000 and other QT variations in terms of Peak Signal To Noise Ratio (PSNR) vs. compression ratio, it is also shown to have competitive Rate- Distortion (RD) performance with other methods whilst reducing program complexity and efficiency. The ILQT is also shown to outperform other QT methods in terms of perceptual quality.