In the past, hypothetical spherical target volumes and ideally conformal dose distributions were analyzed to establish the safety of planning target volume (PTV) margins. In this work we extended these models to estimate how alternative methods of shaping dose distributions could lead to clinical improvements. Based on a spherical clinical target volume (CTV) and Gaussian distributions of systematic and random geometrical uncertainties, idealized 3D dose distributions were optimized to exhibit specific stochastic properties. A nearby spherical organ at risk (OAR) was introduced to explore the benefit of non-spherical dose distributions. Optimizing for the same minimum dose safety criterion as implied by the generally accepted use of a PTV, the extent of the high dose region in one direction could be reduced by half provided that dose in other directions is sufficiently compensated. Further reduction of this unilateral dosimetric margin decreased the target dose confidence, however the actual minimum CTV dose at 90% confidence typically exceeded the minimum PTV dose by 20% of prescription. Incorporation of smooth dose-effect relations within the optimization led to more concentrated dose distributions compared to the use of a PTV, with an improved balance between the probability of tumor cell kill and the risk of geometrical miss, and lower dose to surrounding tissues. Tumor control rate improvements in excess of 20% were found to be common for equal integral dose, while at the same time evading a nearby OAR. These results were robust against uncertainties in dose-effect relations and target heterogeneity, and did not depend on 'shoulders' or 'horns' in the dose distributions.