Deep neural networks (DNNs) have been deployed for many image segmentation tasks and achieved outstanding performance. However, preparing a dataset for training segmentation DNNs is laborious and costly since typically pixel-level annotations are provided for each object of interest. To alleviate this issue, one can provide only weak labels such as bounding boxes or scribbles, or less accurate (noisy) annotations of the objects. These are significantly faster to generate and thus result in more annotated images given the same time budget. However, the reduction in quality might negatively affect the segmentation performance of the resulting model. In this study, we perform a thorough cost-effectiveness evaluation of several weak and noisy labels. We considered 11 variants of annotation strategies and 4 datasets. We conclude that the common practice of accurately outlining the objects of interest is virtually never the optimal approach when the annotation time is limited, even if notable annotation time is available (10s of hours). Annotation approaches that stood out in such scenarios were (1) contour-based annotation with rough continuous traces, (2) polygon-based annotation with few vertices, and (3) box annotations combined with the Segment Anything Model (SAM). In situations where unlimited annotation time was available, precise annotations still lead to the highest segmentation model performance.