Hierarchical pooling in conjunction with Graph Neural Networks (GNN) improves performance in graph classification tasks. Hierarchical pooling has to produce Multi-resolution representations while preserving graph-level information. One such hierarchical pooling is Standard-Sparse-Pooling (SSP). SSP assigns an importance score to each node, selects the Top-K nodes, and scales their attributes by their scores to produce the output. We reveal SSPs’ tendency to pool Over Representative Regions (ORR) on the graph’s signal space leaving some regions unpooled thus proving that SSP is incapable of preserving graph-level information robustly. We propose to overcome this by an improved differentiable exploration over the graph’s signal space dubbed as skipping hence the name SkipPool. We tested SkipPool & its variant SkipPool-Full each against matching pooling methods. Proposed methods achieve new state-of-the-art performance on the majority of benchmark datasets. Moreover, we show that skipping is more robust at capturing the graph signal space consequently preserving more graph-level information than its counterparts. Proposed methods require a reasonably few parameters and their execution time can be kept low with parallelization.