The compression of Electrocardiography (ECG) signals acquired in off-the-person scenarios requires methods that cope with noise and other impairments on the acquisition process. In this paper, after a brief review of common onthe-person ECG signal compression algorithms, we propose and evaluate techniques for this compression task with offthe-person acquired signals, in both lossy and lossless scenarios, evaluated with standard metrics. Our experimental results show that the joint use of Linear Predictive Coding and Lempel-Ziv-Welch is an adequate lossless approach, and the amplitude scaling followed by the Discrete Wavelet Transform achieves the best compression ratio, with a small distortion, among the lossy techniques.