Wavelets and wavelet packets have recently emerged as powerful tools for signal compression. Wavelet and wavelet packet-based compression algorithms based on embedded zerotree wavelet (EZW) coding are developed for electrocardiogram (ECG) signals, and eight different wavelets are evaluated for their ability to compress Holter ECG data. Pilot data from a blind evaluation of compressed ECG's by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECG's are clinically useful.