In recent years, there has been a growing interest in the compression of electroencephalographic (EEG) signals for telemedical and ambulatory EEG applications. Data compression is an important factor in these applications as a means of reducing the amount of data required for transmission. Allowing for a carefully controlled level of loss in the compression method can provide significant gains in data compression. Quantization is an easy to implement method of data reduction that requires little power expenditure. However, it is a relatively simple, noninvertible operation, and reducing the bit-level too far can result in the loss of too much information to reproduce the original signal to an appropriate fidelity. Other lossy compression methods allow for finer control over compression parameters, generally relying on discarding signal components the coder deems insignificant. SPIHT is a state of the art signal compression method based on the Discrete Wavelet Transform (DWT), originally designed for images but highly regarded as a general means of data compression. This paper compares the approaches of compression by changing the quantization level of the DWT coefficients in SPIHT, with the standard thresholding method used in SPIHT, to evaluate the effects of each on EEG signals. The combination of increasing quantization and the use of SPIHT as an entropy encoder has been shown to provide significantly improved results over using the standard SPIHT algorithm alone.