Clinical procedures and legal requirements increasingly demand greater performance in JPEG compression of digitised grayscale medical images without loss of visual fidelity or without exceeding a bounded error metric. Current JPEG common practice uses a default general-purpose luminance quantisation matrix. As an initial investigation into defining more suitable quantisation matrices for different medical image modalities, a new candidate matrix has been derived for mammograms. For a given SNR, the new quantisation matrix achieves a relative compression ratio performance improvement of approximately 22% for a quality factor of 95% and 15% for a quality factor of 85%. This study paves the way for a computationally intelligent approach to optimising the quantisation matrix for each medical image modality in both batch mode and adaptively on an image-by-image basis.