In this article, we focus on rearranging an object by pushing it to any target planar pose. We identify the essential elements to guarantee that the target pose can be reached at an acceptable precision. We present a simple rearrangement algorithm that relies on only a few known straight-line pushes for some novel object and requires no analytical models, force sensors, or large training datasets. We derive the step upper bound, which relates the initial pose of the object, stopping criterion, and quality of the set of pushes, to facilitate the estimation of the maximum number of required steps without the need to perform a task. We experimentally verified the performance of our algorithm at different noise levels, stopping criteria, and task difficulties on datasets containing several types of objects. By applying combinations of only nine known pushes, our simple algorithm performed successfully in real-world experiments with challenging objects, including partially deformable objects that are difficult to model analytically; it achieved the precise stopping criterion (7.5 mm, 5°) in various rearrangement tasks.