Wavelet based data compression methods have demonstrated superior performance over the conventional interpolative methods. However, the wavelet based methods need thresholding on the wavelet domain coefficients. Since wavelet coefficients are not commonly intuitive to engineers, significant a priori knowledge of either the wavelet coefficients or process thresholds is required. So unless thresholds are pre-specified, this requirement makes wavelets unsuitable for on-line implementations. Furthermore, as the relation between the wavelet domain coefficients and the measures of the quality of compression [root mean square error (RMSE) and local point error (LPE)] is not straightforward, it is difficult to achieve good control over the quality of compression by specifying thresholds on the wavelet coefficients. In this paper, an error based criterion is proposed for online wavelet data compression. It uses semantically straightforward measures of the quality of the result to be obtained to adaptively calculate the thresholds. Given a bound on time domain error limits like the RMSE and LPE, this technique adaptively computes the threshold values in wavelet domain. Experiments show that the resulting algorithm gives superior compression as compared to other wavelet based methods. Most importantly, it can be used on-line and provides an effective way of controlling LPE and RMSE. Finally, this method can easily be extended to other on-line wavelet applications such as data rectification and de-noising.