Telecardiology is envisaged as a supplement to inadequate local cardiac care, especially, in infrastructure deficient communities. Yet the associated infrastructure constraints are often ignored while designing a traditional telecardiology system that simply records and transmits user electrocardiogram (ECG) signals to a professional diagnostic facility. Against this backdrop, we propose a two-tier telecardiology framework, where constraints on resources, such as power and bandwidth, are met by compressively sampling ECG signals, identifying anomalous signals, and transmitting only the anomalous signals. Specifically, we design practical compressive classifiers based on inherent properties of ECG signals, such as self-similarity and periodicity, and illustrate their efficacy by plotting receiver operating characteristics (ROC). Using such classifiers, we realize a resource-constrained telecardiology system, which, for the PhysioNet databases, allows no more than 0.5% undetected patients even at an average downsampling factor of five, reducing the power requirement by 80% and bandwidth requirement by 83.4% compared to traditional telecardiology. © 2015 Elsevier Ltd.