The tree of shapes is a hierarchical data structure that models a grey-level image via its level lines. It belongs to the family of morphological trees, which allow to design connected operators, i.e. non-linear filters that transform an image without creating new contours. Connected operators act by modifying the image-modeling tree, shifting the values of its nodes. This paradigm is frequently used with the component tree, another popular morphological tree. It is much less considered in the case of the tree of shapes despite its ability to model more finely the image. Indeed, shifting the values of the nodes of a tree of shapes is more complex, compared to other morphological trees. In this article, we investigate how to modify a tree of shapes by shifting the values of its nodes. We explain how to carry out this operation so that the modified / simplified tree remains the tree of shapes of the processed image. We propose algorithmic solutions and methodological schemes to reach that goal. We discuss on their properties and we illustrate their relevance by application examples of induced connected operators.