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Monitoring and measuring various metrics of high-speed networks produces a vast amount of information over a long period of time making the storage of the metrics a serious issue. Previous work has suggested stream aware compression algorithms, among others, that is, methodologies that try to organise the network packets in a compact way in order to occupy less storage. However, these methods do not reduce the redundancy in the stream information. Lossy compression becomes an attractive solution, as higher compression ratios can be achieved. However, the important and significant elements of the original data need to be preserved. This study proposes the use of a lossy wavelet compression mechanism that preserves crucial statistical and visual characteristics of the examined computer network measurements and provides significant compression against the original file sizes. To the best of authors' knowledge, this is the first study to suggest and implement a wavelet analysis technique for compressing computer network measurements. Here, wavelet analysis is used and compared against the Gzip and Bzip2 tools for data rate and delay measurements. In addition, this study also provides a comparison of eight different wavelets with respect to the compression ratio, the preservation of the scaling behaviour, of the long-range dependence (LRD), of the mean and standard deviation and of the general reconstruction quality. The results show that the Haar wavelet provides higher peak signal-to-noise ratio (PSNR) values and better overall results, than other wavelets with more vanishing moments. Our proposed methodology has been implemented on an online-based measurement platform and compressed data traffic generated from a live network.