In　this　paper,　we　discuss　asymptotic　infimum　coverage　probability　(ICP)　of　eight　widely　used　confidence　intervals　for　proportions,　including　the　Agresti-Coull　(A-C)　interval　(Am　Stat　52:119-126,　1998)　and　the　Clopper-Pearson　(C-P)　interval　(Biometrika　26:404-413,　1934).　For　the　A-C　interval,　a　sharp　upper　bound　for　its　asymptotic　ICP　is　derived.　It　is　less　than　nominal　for　the　commonly　applied　nominal　values　of　0.99,　0.95　and　0.9　and　is　equal　to　zero　when　the　nominal　level　is　below　0.4802.　The　C-P　interval　is　known　to　be　conservative.　However,　we　show　through　a　brief　numerical　study　that　the　C-P　interval　with　a　given　average　coverage　probability　typically　has　a　similar　or　larger　ICP　and　a　smaller　average　expected　length　than　the　corresponding　A-C　interval,　and　its　ICP　approaches　to　when　the　sample　size　goes　large.　All　mathematical　proofs　and　R-codes　for　computation　in　the　paper　are　given　in　Supplementary　Materials.