In multitask learning, conflicts between task gradients are a frequent issue degrading a model’s training performance. This is commonly addressed by using the Gradient Projection algorithm PCGrad that often leads to faster convergence and improved performance metrics. In this work, we present a method to adapt this algorithm to simultaneously also perform task prioritization. Our approach differs from traditional task weighting performed by scaling task losses in that our weighting scheme applies only in cases where tasks are in conflict, but lets the training proceed unhindered otherwise. We replace task weighting factors by a probability distribution that determines which task gradients get projected in conflict cases. Our experiments on the nuScenes, CIFAR-100, and CelebA datasets confirm that our approach is a practical method for task weighting. Paired with multiple different task weighting schemes, we observe significant improvements by up to \(7.2\%\) in the performance metrics of the individual tasks compared to Gradient Projection with uniform projection probabilities.