While self-attention mechanisms in transformers exhibit superior performance in image super-resolution tasks, improving efficiency remains a challenge. To enhance the efficiency of self-attention mechanisms for stereo image super-resolution, we propose an efficient transformer with compressed-attention for stereo image super-resolution (ETCASSR). Specifically, we propose a simple yet effective compressed-attention mechanism that organizes channels from partial to full for attention operations. Using this mechanism, we develop a compressed window-based self-attention block and a compressed transposed self-attention block, enabling efficient intra-view feature extraction. To further enrich feature representation, we introduce a spatial local feature branch and a channel global feature branch to complement these two blocks. Furthermore, a compressed cross-attention block for cross-view feature extraction is designed by extending the compressed-attention mechanism. Combining these blocks, ETCASSR achieves state-of-the-art performance on stereo image super-resolution while maintaining low computational complexity and fast running speed. Additionally, we introduce ETCASR for single-image super-resolution by omitting the cross-view components from ETCASSR, also achieving superior performance with high efficiency. The proposed transformers offer significant potential applications in other vision tasks. Source code is available at https://github.com/jianwensong/ETCASSR.