diff --git a/typed-racket-lib/typed-racket/base-env/base-env-numeric.rkt b/typed-racket-lib/typed-racket/base-env/base-env-numeric.rkt
index fbc6d7b32..d03919e56 100644
--- a/typed-racket-lib/typed-racket/base-env/base-env-numeric.rkt
+++ b/typed-racket-lib/typed-racket/base-env/base-env-numeric.rkt
@@ -134,6 +134,9 @@
       (fx-from-cases
        (-> -Int -Zero -Fixnum : -true-propset : (-arg-path 0))
        (-One -One . -> . -Zero)
+       (-Byte>1 -One . -> . -PosByte)
+       (-Index>1 -One . -> . -PosIndex)
+       (-Int>1 -One . -> . -PosFixnum)
        (-PosByte -One . -> . -Byte)
        (-PosIndex -One . -> . -Index)
        (-PosInt -One . -> . -NonNegFixnum)
@@ -1105,6 +1108,10 @@
 
     (-> N -Zero N : -true-propset : (-arg-path 0))
     (-> -One -One -Zero)
+    (-> -Byte>1 -One -PosByte)
+    (-> -Index>1 -One -PosIndex)
+    (-> -Fixnum>1 -One -PosFixnum)
+    (-> -Int>1 -One -PosInt)
     (-> -PosByte -One -Byte)
     (-> -PosIndex -One -Index)
     (-> -PosFixnum -One -NonNegFixnum)
@@ -1291,6 +1298,10 @@
 
 [sub1 (from-cases
        (-> -One -Zero)
+       (-> -Byte>1 -PosByte)
+       (-> -Index>1 -PosIndex)
+       (-> -Fixnum>1 -PosFixnum)
+       (-> -Int>1 -Pos)
        (-> -PosByte -Byte)
        (-> -PosIndex -Index)
        (-> -Index -Fixnum)
diff --git a/typed-racket-lib/typed-racket/types/numeric-tower.rkt b/typed-racket-lib/typed-racket/types/numeric-tower.rkt
index 590bc33e3..89f48d444 100644
--- a/typed-racket-lib/typed-racket/types/numeric-tower.rkt
+++ b/typed-racket-lib/typed-racket/types/numeric-tower.rkt
@@ -10,9 +10,9 @@
          (for-template racket/base racket/contract/base (types numeric-predicates)))
 
 (provide portable-fixnum? portable-index?
-         -Zero -One -PosByte -Byte -PosIndex -Index
-         -PosFixnum -NonNegFixnum -NegFixnum -NonPosFixnum -Fixnum
-         -PosInt -Nat -NegInt -NonPosInt -Int
+         -Zero -One -Byte>1 -PosByte -Byte -Index>1 -PosIndex -Index
+         -Fixnum>1 -PosFixnum -NonNegFixnum -NegFixnum -NonPosFixnum -Fixnum
+         -Int>1 -PosInt -Nat -NegInt -NonPosInt -Int
          -PosRat -NonNegRat -NegRat -NonPosRat -Rat
          -FlonumPosZero -FlonumNegZero -FlonumZero -FlonumNan
          -PosFlonum -NonNegFlonum -NegFlonum -NonPosFlonum -Flonum
@@ -46,15 +46,18 @@
 (define/decl -PosByte (Un -One -Byte>1))
 (define/decl -Byte    (Un -Zero -PosByte))
 
-(define/decl -PosIndex    (Un -One -Byte>1 -PosIndexNotByte))
+(define/decl -Index>1     (Un -Byte>1 -PosIndexNotByte))
+(define/decl -PosIndex    (Un -One -Index>1))
 (define/decl -Index       (Un -Zero -PosIndex))
 
+(define/decl -Fixnum>1     (Un -PosFixnumNotIndex -Index>1))
 (define/decl -PosFixnum    (Un -PosFixnumNotIndex -PosIndex))
 (define/decl -NonNegFixnum (Un -PosFixnum -Zero))
 
 (define/decl -NonPosFixnum (Un -NegFixnum -Zero))
 (define/decl -Fixnum       (Un -NegFixnum -Zero -PosFixnum))
 
+(define/decl -Int>1     (Un -PosIntNotFixnum -Fixnum>1))
 (define/decl -PosInt    (Un -PosIntNotFixnum -PosFixnum))
 (define/decl -NonNegInt (Un -PosInt -Zero))
 (define/decl -Nat -NonNegInt)
@@ -132,6 +135,7 @@
           (BaseUnion-nbits -Byte) (cons 0 255)
           (BaseUnion-nbits -PosByte) (cons 1 255)
           (Base-bits -Byte>1) (cons 2 255)
+          (BaseUnion-nbits -Int>1) (cons 2 #f)
           (BaseUnion-nbits -PosInt) (cons 1 #f)
           (BaseUnion-nbits -Nat) (cons 0 #f)
           (BaseUnion-nbits -NonPosInt) (cons #f 0)
@@ -158,12 +162,15 @@
           (BaseUnion-nbits -Byte) (cons 0 255)
           (BaseUnion-nbits -PosByte) (cons 1 255)
           (Base-bits -Byte>1) (cons 2 255)
+          (BaseUnion-nbits -Int>1) (cons 2 #f)
           (BaseUnion-nbits -PosInt) (cons 1 #f)
           (BaseUnion-nbits -Nat) (cons 0 #f)
           (BaseUnion-nbits -NonPosInt) (cons #f 0)
           (BaseUnion-nbits -NegInt) (cons #f -1)
           (BaseUnion-nbits -Index) (cons 0 #f)
+          (BaseUnion-nbits -Index>1) (cons 2 #f)
           (BaseUnion-nbits -PosIndex) (cons 1 #f)
+          (BaseUnion-nbits -Fixnum>1) (cons 2 #f)
           (BaseUnion-nbits -PosFixnum) (cons 1 #f)
           (BaseUnion-nbits -NonNegFixnum) (cons 0 #f)
           (BaseUnion-nbits -NonPosFixnum) (cons #f 0)
@@ -179,9 +186,10 @@
 
 (define all-bounded-int-types
   ;; relies on numeric bits being eq?
-  (for/hasheq ([t (in-list (list -Zero -One -PosByte -Byte>1 -Byte -PosIndex -Index
-                                 -PosFixnum -NonNegFixnum -NegFixnum -NonPosFixnum
-                                 -PosInt -Nat -NegInt -NonPosInt))])
+  (for/hasheq ([t (in-list (list -Zero -One -PosByte -Byte>1 -Byte
+                                 -Index>1 -PosIndex -Index
+                                 -Fixnum>1 -PosFixnum -NonNegFixnum -NegFixnum -NonPosFixnum
+                                 -Int>1 -PosInt -Nat -NegInt -NonPosInt))])
     (values (if (BaseUnion? t)
                 (BaseUnion-nbits t)
                 (Base-bits t))
diff --git a/typed-racket-test/succeed/sub1-int-gt-1.rkt b/typed-racket-test/succeed/sub1-int-gt-1.rkt
new file mode 100644
index 000000000..e9c135ca8
--- /dev/null
+++ b/typed-racket-test/succeed/sub1-int-gt-1.rkt
@@ -0,0 +1,13 @@
+#lang typed/racket
+
+;; From this stack overflow question by Lyu Yao Ting:
+;; Type mismatch issue of sub1
+;; https://stackoverflow.com/questions/58887937/type-mismatch-issue-of-sub1
+
+(define-predicate one? One)
+(: pick1 (-> Positive-Integer (Listof Any) Any))
+(define pick1
+  (λ (n lat)
+    (cond [(one? n) (car lat)]
+          [else (pick1 (sub1 n)
+                       (cdr lat))])))