Recent　developments　in　the　field　of　non-local　attention　(NLA)　have　led　to　a　renewed　interest　in　self-similarity-based　single　image　super-resolution　(SISR).　Researchers　usually　use　the　NLA　to　explore　non-local　self-similarity　(NSS)　in　SISR　and　achieve　satisfactory　reconstruction　results.　However,　a　surprising　phenomenon　that　the　reconstruction　performance　of　the　standard　NLA　is　similar　to　that　of　the　NLA　with　randomly　selected　regions　prompted　us　to　revisit　NLA.　In　this　paper,　we　first　analyzed　the　attention　map　of　the　standard　NLA　from　different　perspectives　and　discovered　that　the　resulting　probability　distribution　always　has　full　support　for　every　local　feature,　which　implies　a　statistical　waste　of　assigning　values　to　irrelevant　non-local　features,　especially　for　SISR　which　needs　to　model　long-range　dependence　with　a　large　number　of　redundant　non-local　features.　Based　on　these　findings,　we　introduced　a　concise　yet　effective　soft　thresholding　operation　to　obtain　high-similarity-pass　attention　(HSPA),　which　is　beneficial　for　generating　a　more　compact　and　interpretable　distribution.　Furthermore,　we　derived　some　key　properties　of　the　soft　thresholding　operation　that　enable　training　our　HSPA　in　an　end-to-end　manner.　The　HSPA　can　be　integrated　into　existing　deep　SISR　models　as　an　efficient　general　building　block.　In　addition,　to　demonstrate　the　effectiveness　of　the　HSPA,　we　constructed　a　deep　high-similarity-pass　attention　network　(HSPAN)　by　integrating　a　few　HSPAs　in　a　simple　backbone.　Extensive　experimental　results　demonstrate　that　HSPAN　outperforms　state-of-the-art　approaches　on　both　quantitative　and　qualitative　evaluations.　Our　code　and　a　pre-trained　model　were　uploaded　to　GitHub　(https://github.com/laoyangui/HSPAN)　for　validation.　©　1992-2012　IEEE.