diff --git a/pkgs/racket-test-core/tests/racket/unicode.rktl b/pkgs/racket-test-core/tests/racket/unicode.rktl
index 95b2a29ec5..eb2aa1c6de 100644
--- a/pkgs/racket-test-core/tests/racket/unicode.rktl
+++ b/pkgs/racket-test-core/tests/racket/unicode.rktl
@@ -628,25 +628,39 @@
 		    [s (apply bytes (caddr p))])
 		(if (and (positive? (vector-length code-points))
 			 (vector-ref code-points 0))
-		    (begin
-		      (test (vector-length code-points) bytes-utf-8-length s)
+		    (let ([len (vector-length code-points)]
+                          [c0 (integer->char (vector-ref code-points 0))])
+		      (test len bytes-utf-8-length s)
+		      (test len bytes-utf-8-length s #f)
+		      (test len bytes-utf-8-length s #\x)
+		      (test len bytes-utf-8-length s #f 0)
+		      (test len bytes-utf-8-length s #f 0 (bytes-length s))
+		      (test (sub1 len) bytes-utf-8-length s #f (char-utf-8-length c0) (bytes-length s))
+		      (test (sub1 len) bytes-utf-8-length s #f 0 (- (bytes-length s)
+                                                                    (char-utf-8-length
+                                                                     (integer->char
+                                                                      (vector-ref code-points (sub1 len))))))
 		      (test code-points bytes->unicode-vector s)
 		      (test code-points bytes-any->unicode-vector s #f)
 		      (test s unicode-vector->bytes code-points)
 		      (test 0 bytes-utf-8-index s 0)
-		      (test (bytes-length s) bytes-utf-8-index 
-			    (bytes-append s #"x")
-			    (vector-length code-points))
-		      (if ((vector-length code-points) . > . 1)
+		      (test 0 bytes-utf-8-index s 0 #f)
+		      (test 0 bytes-utf-8-index s 0 #\x)
+		      (test 0 bytes-utf-8-index s 0 #f 0)
+                      (when (len . > . 1)
+                        (test (char-utf-8-length c0) bytes-utf-8-index s 1 #f 0)
+                        (test (char-utf-8-length c0) bytes-utf-8-index s 0 #f (char-utf-8-length c0)))
+                      (test (char-utf-8-length c0) bytes-utf-8-index (bytes-append s #"x") 1 #f 0)
+                      (test (char-utf-8-length c0) bytes-utf-8-index (bytes-append s #"x") 0 #f (char-utf-8-length c0))
+		      (test 0 bytes-utf-8-index s 0 #f 0 (bytes-length s))
+		      (test #f bytes-utf-8-index s 0 #f (bytes-length s))
+		      (test (bytes-length s) bytes-utf-8-index (bytes-append s #"x") len)
+		      (if (len . > . 1)
 			  (begin
-			    (test (integer->char (vector-ref code-points 0))
-				  bytes-utf-8-ref s 0)
-			    (test (integer->char (vector-ref code-points 0))
-				  bytes-utf-8-ref s 0 #f)
-			    (test (integer->char (vector-ref code-points 0))
-				  bytes-utf-8-ref s 0 #f 0)
-			    (test (integer->char (vector-ref code-points 0))
-				  bytes-utf-8-ref s 0 #f 0 (bytes-length s))
+			    (test c0 bytes-utf-8-ref s 0)
+			    (test c0 bytes-utf-8-ref s 0 #f)
+			    (test c0 bytes-utf-8-ref s 0 #f 0)
+			    (test c0 bytes-utf-8-ref s 0 #f 0 (bytes-length s))
 			    (test (integer->char (vector-ref code-points
 							     (sub1 (vector-length code-points))))
 				  bytes-utf-8-ref s (sub1 (vector-length code-points)))
diff --git a/racket/src/io/string/convert.rkt b/racket/src/io/string/convert.rkt
index df61d52d3e..df698e16b1 100644
--- a/racket/src/io/string/convert.rkt
+++ b/racket/src/io/string/convert.rkt
@@ -83,7 +83,7 @@
     [(eq? state 'continues)
      (cond
        [(and get-index? ((+ start initial-used-bytes) . < . end))
-        initial-used-bytes]
+        (+ initial-used-bytes start)]
        [else
         ;; Get one more byte
         (define str (and (not get-index?) (make-string 1)))
@@ -98,7 +98,7 @@
                (or (and (eq? state 'complete)
                         (= got-chars 1))))
            (if get-index?
-               initial-used-bytes
+               (+ initial-used-bytes start)
                (string-ref str 0))]
           [else #f])])]
     [else #f]))
diff --git a/racket/src/racket/src/string.c b/racket/src/racket/src/string.c
index 48a3ce1645..9ffd8d2091 100644
--- a/racket/src/racket/src/string.c
+++ b/racket/src/racket/src/string.c
@@ -664,7 +664,7 @@ scheme_init_string (Scheme_Startup_Env *env)
   SCHEME_PRIM_PROC_FLAGS(p) |= scheme_intern_prim_opt_flags(SCHEME_PRIM_AD_HOC_OPT);
   scheme_addto_prim_instance("bytes->immutable-bytes", p, env);
 
-  p = scheme_make_immed_prim(byte_string_utf8_index, "bytes-utf-8-index", 2, 4);
+  p = scheme_make_immed_prim(byte_string_utf8_index, "bytes-utf-8-index", 2, 5);
   /* Incorrect, since the result can be #f:
      SCHEME_PRIM_PROC_FLAGS(p) |= scheme_intern_prim_opt_flags(SCHEME_PRIM_PRODUCES_FIXNUM); */
   scheme_addto_prim_instance("bytes-utf-8-index", p, env);