For magnetic resonance imaging of tissues with very short transverse relaxation times, radio-frequency excitation must be immediately followed by data acquisition with fast spatial encoding. In zero-echo-time (ZTE) imaging, excitation is performed while the readout gradient is already on, causing data loss due to an initial dead time. One major dead time contribution is the settling time of the filters involved in signal down-conversion. In this paper, a multi-rate acquisition scheme is proposed to minimize dead time due to filtering. Short filters and high output bandwidth are used initially to minimize settling time. With increasing time since the signal onset, longer filters with better frequency selectivity enable stronger signal decimation. In this way, significant dead time reduction is accomplished at only a slight increase in the overall amount of output data. Multi-rate acquisition was implemented with a two-stage filter cascade in a digital receiver based on a field-programmable gate array. In ZTE imaging in a phantom and in vivo, dead time reduction by multi-rate acquisition is shown to improve image quality and expand the feasible bandwidth while increasing the amount of data collected by only a few percent.