Remote health monitoring by exploiting wireless communications technologies is an emerging area receiving increasing interests from academia, research labs and industry. This issue has also been brought up in the standardization process of IEEE 802.15 Task Group 6 Wireless Body Area Networks (WBAN). The challenge is to find the appropriate combination of medical data processing techniques and the wireless technology in order to meet the particularly stringent error, latency and power consumption requirements of healthcare applications. In this paper, we present the results of a case study on wireless electrocardiogram (ECG) monitoring over Bluetooth. Based on the special considerations of (processing and transmission) power consumption at wireless ECG sensors, we first propose a low complexity ECG compression method. Comparisons with existing approaches confirm the superior performance of our method. We then study the data reconstruction performance at the Bluetooth receiver and find that: i) the uncompressed ECG data transmission is not necessarily better than the compressed transmission; and ii) there exists an optimum ECG data compression ratio for the wireless link.