A simple approach to improve the performance of JPEG is proposed. In JPEG, quantized ac coefficients at high frequency generally have zero or small energies. Thus they contribute little or nothing to the peak signal-to-noise ratio (PSNR). This implies that the bit rate can be reduced by discarding some high-frequency ac coefficients with little or no loss in PSNR. Based on this idea, we incorporate the concept of zonal coding into JPEG. This proposal is termed the zonal JPEG. In it, the coding scheme is identical to that of the traditional JPEG except that only a fixed number of coefficients are coded for each image block. Consequently, the proposed approach is totally compatible with the traditional JPEG. It has two advantages over the latter: (i) better bit-rate utilization and (ii) achievable user-defined PSNR. These advantages have been verified by simulation results.