In this note we present strategies to improve the quality of adaptive FE-approximations measured in terms of linear functionals. The ideas are based on the so called dual-weighted-residual (DWR) approach to a posteriori error control for FE-schemes. In more details, we exploit those parts of an underlying error representation, which are completely computable, to improve the FE-solution.Furthermore, the remaining parts of the error identity can be estimated  by well established a posteriorienergy estimates yielding reliable error bounds for the postprocessed values.