U-Net architectures have been instrumental in advancing biomedical image segmentation (BIS) but often struggle with capturing long-range information. One reason is the conventional down-sampling techniques that prioritize computational efficiency at the expense of information retention. This paper introduces a simple but effective strategy, we call it Stair Pooling, which moderates the pace of down-sampling and reduces information loss by leveraging a sequence of concatenated small and narrow pooling operations in varied orientations. Specifically, our method modifies the reduction in dimensionality within each 2D pooling step from $\frac{1}{4}$ to $\frac{1}{2}$. This approach can also be adapted for 3D pooling to preserve even more information. Such preservation aids the U-Net in more effectively reconstructing spatial details during the up-sampling phase, thereby enhancing its ability to capture long-range information and improving segmentation accuracy. Extensive experiments on three BIS benchmarks demonstrate that the proposed Stair Pooling can increase both 2D and 3D U-Net performance by an average of 3.8\% in Dice scores. Moreover, we leverage the transfer entropy to select the optimal down-sampling paths and quantitatively show how the proposed Stair Pooling reduces the information loss.