diff --git a/collects/tests/typed-racket/unit-tests/typecheck-tests.rkt b/collects/tests/typed-racket/unit-tests/typecheck-tests.rkt
index dc244ff243..5d6a4ada3c 100644
--- a/collects/tests/typed-racket/unit-tests/typecheck-tests.rkt
+++ b/collects/tests/typed-racket/unit-tests/typecheck-tests.rkt
@@ -266,6 +266,9 @@
                     (when (boolean? x) #t))
               -Void]
 
+        [tc-e (integer-bytes->integer '#"abcd" #t) -Nat]
+        [tc-e (integer-bytes->integer '#"abcd" #f) -Int]
+
         [tc-e/t (let: ([x : Any 3])
                     (if (list? x)
                         (begin (car x) 1)
diff --git a/collects/typed-racket/base-env/base-env-indexing-abs.rkt b/collects/typed-racket/base-env/base-env-indexing-abs.rkt
index ac1c76c32d..23c12c1e9f 100644
--- a/collects/typed-racket/base-env/base-env-indexing-abs.rkt
+++ b/collects/typed-racket/base-env/base-env-indexing-abs.rkt
@@ -303,7 +303,14 @@
    [bytes-utf-8-index (-Bytes [index-type (Un (-val #f) -Char) index-type index-type] . ->opt . -Index)]
 
    [integer->integer-bytes (-Integer index-type Univ [Univ -Bytes index-type] . ->opt . -Bytes)]
-   [integer-bytes->integer (-Bytes Univ [Univ index-type index-type] . ->opt . -Integer)]
+   [integer-bytes->integer
+    (cl->*
+     ;; Any truthy value (not only #t) would work here.
+     ;; We can define a truthy type (without difference types (- Univ #f))
+     ;; by unioning everything (including StructTop and co).
+     ;; We should do this at some point.
+     (-Bytes (-val #t) [Univ index-type index-type] . ->opt . -Nat)
+     (-Bytes Univ [Univ index-type index-type] . ->opt . -Integer))]
 
    [peek-char
     (cl->* [->opt [-Input-Port index-type] (Un -Char (-val eof))])]
diff --git a/collects/typed-racket/base-env/base-env-numeric.rkt b/collects/typed-racket/base-env/base-env-numeric.rkt
index cb25ff614b..e2ab30be81 100644
--- a/collects/typed-racket/base-env/base-env-numeric.rkt
+++ b/collects/typed-racket/base-env/base-env-numeric.rkt
@@ -1352,9 +1352,11 @@
   (-NonPosInt -Int . -> . (-values (list -Int -NonPosInt)))
   (-Int -Int . -> . (-values (list -Int -Int))))]
 
-[arithmetic-shift (cl->* (-Zero (Un -NegFixnum -Zero) . -> . -Zero)
-                         (-NonNegFixnum (Un -NegFixnum -Zero) . -> . -NonNegFixnum)
-                         (-Fixnum (Un -NegFixnum -Zero) . -> . -Fixnum)
+[arithmetic-shift (cl->* (-Zero -NonPosInt . -> . -Zero)
+                         (-Byte -NonPosInt . -> . -Byte)
+                         (-Index -NonPosInt . -> . -Index)
+                         (-NonNegFixnum -NonPosInt . -> . -NonNegFixnum)
+                         (-Fixnum -NonPosInt . -> . -Fixnum)
                          (-Nat -Int . -> . -Nat)
                          (-Int -Int . -> . -Int))]