A flexible maximum-entropy component separation algorithm is presented that accommodates anisotropic noise , incomplete sky-coverage and uncertainties in the spectral parameters of foregrounds . The capabilities of the method are determined by first applying it to simulated spherical microwave data sets emulating the COBE-DMR , COBE-DIRBE and Haslam surveys . Using these simulations we find that is very difficult to determine unambiguously the spectral parameters of the galactic components for this data set due to their high level of noise . Nevertheless , we show that is possible to find a robust CMB reconstruction , especially at the high galactic latitude . The method is then applied to these real data sets to obtain reconstructions of the CMB component and galactic foreground emission over the whole sky . The best reconstructions are found for values of the spectral parameters : T _ { d } = 19 K , \alpha _ { d } = 2 , \beta _ { ff } = -0.19 and \beta _ { syn } = -0.8 . The CMB map has been recovered with an estimated statistical error of \sim 22 \mu K on an angular scale of 7 degrees outside the galactic cut whereas the low galactic latitude region presents contamination from the foreground emissions .