The quantization of the discrete wavelet transform (DWT) coefficients in the still image compression is the main topic of this work. An overview of the wavelet theory is given, the usage of the two-dimensional DWT in the still image compression is shown, and advantages of the wavelet coders over the coder with the discrete cosine transform are discussed. Stastistical characteristics of the wavelet subbands are analysed. The general Gaussian function is a good approximation of the probability density function (PDF) of the wavelet coefficients, and it is also shown here that the parameter k of this function significantly differs from values 0.7 and 1, that are most often mentioned in literature. Parameter k, which influences the PDF shape, mostly depends on an image content. However, the trend of increasing values of k for higher decomposition levels and higher values of k for diagonally orientated subbands, is established. A new, fast method is presented for a good parameter k estimation from the statistics of wavelet coefficients for every individual subband. On the basis of the scalar quantization and subband coding theory an algorithm is developed for the estimation of the optimal quantization step for the purpose of achieving the maximum signal to noise ratio (S/N) for the given bit rate in the procedure of image compression. It was found out that the effects of increasing the standard deviation and amplitude dynamics of subbands have opposite influences on the optimal quantization step magnitude. That results in the optimal behaviour (in the S/N sense) of the uniform scalar quantization with the identical quantization step for all subbands, for this type of the coder. In order to make the most of the reduced sensitivity of the human visual system to higher frequencies, an application of the visually weighted quantization is investigated. For that purpose, measurements of the wavelet quantization noise are carried out for five different wavelets. By introducing a new wavelet visual weighting function a theoretical foundation is set for a connection between the quantization noise visibility threshold defined by measuring and the wavelet filters frequency response. By using a genetic algorithm, parameters of the visual weighting function are estimated, and a good correspondence between theoretical and measured results is established. The possibility of the visually weighted quantization steps calculation is established for the wavelets which are not included by this measurement. The images compression carried out with the visually weighted quantization determined according to measurement results gave good visual quality as well as a better S/N in relation to known visually tuned quantization matrices.