Compression of electrocardiograms (ECG) in wireless environments, with diagnostic quality, has shown limited potential. This lack of quality preservation, using Wavelet Transform (WT), is due to the fact that the multiple levels of detail that can be achieved in the time domain are not exploited. In the present work, we propose to fully exploit the wavelet capability to operate at different levels of signal detail at different time scales. WT with an appropriate Compressed Sensing (CS) matrix is used in the electrode nodes of body sensor networks to encode and compress the ECG. Then, the signal is reconstructed using a basis pursuit denoise algorithm. Preservation of the diagnostic quality by means of standardized metrics is then tested for multiple wavelet bases and levels. High quality ECGs from 50 healthy patients are used to statistically show that diagnostic quality preservation is possible even at high compression rates. In these cases suitable ECG wavelets are required.