diff --git a/pkgs/racket-test/tests/racket/contract/name.rkt b/pkgs/racket-test/tests/racket/contract/name.rkt
index fe00bc11bf..273462554e 100644
--- a/pkgs/racket-test/tests/racket/contract/name.rkt
+++ b/pkgs/racket-test/tests/racket/contract/name.rkt
@@ -266,6 +266,8 @@
   (test-name 'exact-positive-integer? (integer-in 1 #f))
   (test-name '(char-in #\a #\z) (char-in #\a #\z))
   (test-name '(and/c 0 exact?) (integer-in 0 0))
+  ;; this next one is convenient, using the and/c name would also be okay
+  (test-name '(integer-in 0 9) (and/c (</c 10) exact-integer? (>=/c 0)))
   (test-name '(real-in 1 10) (real-in 1 10))
   (test-name '(between/c 1 10) (between/c 1 10))
   (test-name '(string-len/c 3) (string-len/c 3))
diff --git a/pkgs/racket-test/tests/racket/contract/stronger.rkt b/pkgs/racket-test/tests/racket/contract/stronger.rkt
index b8b55af941..3afa823ad0 100644
--- a/pkgs/racket-test/tests/racket/contract/stronger.rkt
+++ b/pkgs/racket-test/tests/racket/contract/stronger.rkt
@@ -23,6 +23,13 @@
   (ctest #t contract-stronger? (integer-in #f 0) (integer-in #f #f))
   (ctest #t contract-stronger? (integer-in 0 0) (and/c 0 exact?))
   (ctest #t contract-stronger? (and/c 0 exact?) (integer-in 0 0))
+  (ctest #t contract-stronger? (and/c exact-integer? (>=/c 1) (<=/c 10)) (integer-in 1 10))
+  (ctest #t contract-stronger? (integer-in 1 10) (and/c exact-integer? (>=/c 1) (<=/c 10)))
+  (ctest #t contract-stronger? (and/c exact-integer? (<=/c 10) (>/c 1)) (integer-in 2 10))
+  (ctest #t contract-stronger? (integer-in 2 10) (and/c exact-integer? (<=/c 10) (>/c 1)))
+  (ctest #t contract-stronger? (and/c exact-integer? (</c 10) (>/c 1)) (integer-in 2 9))
+  (ctest #t contract-stronger? (integer-in 2 9) (and/c exact-integer? (</c 10) (>/c 1)))
+  (ctest #t contract-stronger? (integer-in 2 9) (and/c exact-integer? (</c 10.0) (>/c 1.0)))
   (ctest #t contract-stronger? exact-integer? (integer-in #f #f))
   (ctest #t contract-stronger? (integer-in #f #f) exact-integer?)
   (ctest #t contract-stronger? (integer-in 0 #f) exact-nonnegative-integer?)
diff --git a/racket/collects/racket/contract/private/and.rkt b/racket/collects/racket/contract/private/and.rkt
index 843f65ebff..f7aa7a0fd0 100644
--- a/racket/collects/racket/contract/private/and.rkt
+++ b/racket/collects/racket/contract/private/and.rkt
@@ -247,6 +247,36 @@
                [else (make-first-order-and/c contracts preds)])]
             [else
              (make-first-order-and/c contracts preds)])]
+         [(and (pair? (cdr preds))
+               (pair? (cddr preds))
+               (null? (cdddr preds)))
+          (cond
+            [(or (chaperone-of? (car preds) exact-integer?)
+                 (chaperone-of? (cadr preds) exact-integer?)
+                 (chaperone-of? (caddr preds) exact-integer?))
+             (define lb #f)
+             (define ub #f)
+             (for ([ctc (in-list contracts)])
+               (cond
+                 [(between/c-s? ctc)
+                  (define lo (between/c-s-low ctc))
+                  (define hi (between/c-s-high ctc))
+                  (cond
+                    [(and (= lo -inf.0) (integer? hi))
+                     (set! ub (inexact->exact hi))]
+                    [(and (= hi +inf.0) (integer? lo))
+                     (set! lb (inexact->exact lo))])]
+                 [(</>-ctc? ctc)
+                  (define x (</>-ctc-x ctc))
+                  (when (integer? x)
+                    (cond
+                      [(<-ctc? ctc) (set! ub (- (inexact->exact x) 1))]
+                      [(>-ctc? ctc) (set! lb (+ (inexact->exact x) 1))]))]))
+             (cond
+               [(and lb ub)
+                (integer-in lb ub)]
+               [else (make-first-order-and/c contracts preds)])]
+            [else (make-first-order-and/c contracts preds)])]
          [else
           (make-first-order-and/c contracts preds)])]
       [(andmap chaperone-contract? contracts)
diff --git a/racket/collects/racket/contract/private/misc.rkt b/racket/collects/racket/contract/private/misc.rkt
index cf1885bfa2..ddd22cb88b 100644
--- a/racket/collects/racket/contract/private/misc.rkt
+++ b/racket/collects/racket/contract/private/misc.rkt
@@ -58,6 +58,9 @@
          flat-contract-with-explanation
 
          (struct-out between/c-s)
+         (struct-out </>-ctc)
+         (struct-out <-ctc)
+         (struct-out >-ctc)
          renamed-between/c)
 
 (define-syntax (flat-murec-contract stx)