Future large scale cosmological surveys will provide huge data sets whose analysis requires efficient data compression. Calculating accurate covariances is extremely challenging with increasing number of statistics used. Here we introduce a formalism for achieving efficient data compression, based on a local expansion of statistical measures around a fiducial cosmological model. We specifically apply and test this approach for the case of cosmic shear statistics. We demonstrate the performance of our approach, using a Fisher analysis on cosmic shear tomography described in terms of E-/B-mode separating statistics (COSEBIs). We show that our data compression is highly effective in extracting essentially the full cosmological information from a strongly reduced number of observables. Specifically, the number of statistics needed decreases by at least one order of magnitude relative to the COSEBIs, which already compress the data substantially compared to the shear two-point correlation functions. The efficiency appears to be affected only slightly if a highly inaccurate covariance is used for defining the compressed statistics, showing the robustness of the method. We conclude that an efficient data compression is achievable and that the number of compressed statistics depends on the number of model parameters. In addition, we study how well band powers can be obtained from measuring shear correlation functions over a finite interval of separations. We show the strong limitations on the possibility to construct top-hat filters in Fourier space, for which the real-space analog has a finite support, yielding strong bounds on the accuracy of band power estimates. The error on an estimated band-power is larger for a narrower filter and a smaller angular range which for relevant cases can be as large as 10%.