Incomplete tomographic data sets such as limited view missing wedge data represent a well known challenge for reconstruction algorithms, since they unavoidably lead to substantial image artefacts. Such data sets may occur in industrial computed tomography of limited access e.g. extended components, fixed objects , directional opacity, limited sample life time or laminographic set up. We present strategies to effectively suppress the typical elongation artefacts e.g. lemon like deformed pores by our iterative algorithm DIRECTT which offers the opportunity to vary the versatile reconstruction parameters within each cycle. Those strategies are applied to experimental data obtained from metallic foams as well as model simulations. Co...