diff --git a/racket/src/io/common/check.rkt b/racket/src/io/common/check.rkt
index 7c0c5af920..aa0294f451 100644
--- a/racket/src/io/common/check.rkt
+++ b/racket/src/io/common/check.rkt
@@ -20,7 +20,7 @@
             (end-pos . > . max-end))
     (raise-range-error who
                        "byte string"
-                       "starting "
+                       "ending "
                        end-pos
                        in-value
                        0
diff --git a/racket/src/regexp/demo.rkt b/racket/src/regexp/demo.rkt
index 5780283617..3089217198 100644
--- a/racket/src/regexp/demo.rkt
+++ b/racket/src/regexp/demo.rkt
@@ -51,6 +51,30 @@
   (rx:regexp-match "[abc]" in 0 1 discard2 #"")
   (test (get-output-bytes discard2) #" "))
 
+;; Input streams that are large enough for bytes to be discarded along the way
+(test (rx:regexp-match #"(.)x" (open-input-string (string-append (make-string 50000 #\y) "x")))
+      '(#"yx" #"y"))
+(test (rx:regexp-match-positions #"(.)x" (open-input-string (string-append (make-string 50000 #\y) "x")))
+      '((49999 . 50001) (49999 . 50000)))
+(test (rx:regexp-match "(.)x" (string-append (make-string 50000 #\y) "x"))
+      '("yx" "y"))
+(test (rx:regexp-match-positions "(.)x" (string-append (make-string 50000 #\y) "x"))
+      '((49999 . 50001) (49999 . 50000)))
+(test (rx:regexp-match "(.)\u3BC" (string-append (make-string 50000 #\u3BB) "\u3BC"))
+      '("\u3BB\u3BC" "\u3BB"))
+(test (rx:regexp-match-positions "(.)\u3BC" (string-append (make-string 50000 #\y) "\u3BC"))
+      '((49999 . 50001) (49999 . 50000)))
+
+(test (rx:regexp-match-positions #"<([abc])(>)?" "<a + <b = <c" 3)
+      '((5 . 7) (6 . 7) #f))
+(test (rx:regexp-match-positions "[abc]" " a b c " 2)
+      '((3 . 4)))
+(test (rx:regexp-match-positions "(?m:^.\n)" "a\nb\nc\n" 2 6 #f #"\n")
+      '((2 . 4)))
+
+(test (regexp-replace* "-" "zero-or-more?" "_")
+      "zero_or_more?")
+
 ;; ----------------------------------------
 
 (define (check rx in N [M (max 1 (quotient N 10))])
diff --git a/racket/src/regexp/match/extract.rkt b/racket/src/regexp/match/extract.rkt
index b7f5a1333d..7d7aedf58e 100644
--- a/racket/src/regexp/match/extract.rkt
+++ b/racket/src/regexp/match/extract.rkt
@@ -8,6 +8,8 @@
          
          byte-positions->string-positions
          byte-positions->strings
+
+         byte-index->string-index
          
          add-end-bytes)
 
@@ -27,18 +29,19 @@
 
 (define (byte-positions->bytess in ms-pos me-pos state
                                 #:delta [delta 0])
-  (cons (subbytes in (+ ms-pos delta) (+ me-pos delta))
+  (cons (subbytes in (- ms-pos delta) (- me-pos delta))
         (if state
             (for/list ([p (in-vector state)])
               (and p
-                   (subbytes in (+ (car p) delta) (+ (cdr p) delta))))
+                   (subbytes in (- (car p) delta) (- (cdr p) delta))))
             null)))
 
 (define (byte-positions->string-positions bstr-in ms-pos me-pos state
-                                          #:start-offset start-offset
-                                          #:start-pos [start-pos 0])
+                                          #:start-index [start-index 0]
+                                          #:delta [delta 0]
+                                          #:result-offset [result-offset 0])
   (define (string-offset pos)
-    (+ start-offset (bytes-utf-8-length bstr-in #\? start-pos pos)))
+    (+ result-offset (bytes-utf-8-length bstr-in #\? start-index (- pos delta))))
   (cons (cons (string-offset ms-pos) (string-offset me-pos))
         (if state
             (for/list ([p (in-vector state)])
@@ -49,13 +52,32 @@
 
 (define (byte-positions->strings bstr-in ms-pos me-pos state
                                  #:delta [delta 0])
-  (cons (bytes->string/utf-8 bstr-in #\? (+ ms-pos delta) (+ me-pos delta))
+  (cons (bytes->string/utf-8 bstr-in #\? (- ms-pos delta) (- me-pos delta))
         (if state
             (for/list ([p (in-vector state)])
               (and p
-                   (bytes->string/utf-8 bstr-in #\? (+ (car p) delta) (+ delta (cdr p)))))
+                   (bytes->string/utf-8 bstr-in #\? (- (car p) delta) (- (cdr p) delta))))
             null)))
 
+(define (byte-index->string-index str pos)
+  ;; We assume that pos is on a code-point boundary in the
+  ;; UTF-8 encoding of str. Find out how many code points
+  ;; are before the index.
+  (let loop ([lo-pos 0] [lo 0] [hi (min (string-length str)
+                                        (* pos 6))])
+    (cond
+      [(= lo hi) lo]
+      [(= (add1 lo) hi)
+       (if (= lo-pos pos) lo hi)]
+      [else
+       (define mid (quotient (+ lo hi) 2))
+       (define len (string-utf-8-length str lo mid))
+       (define mid-pos (+ lo-pos len))
+       (cond
+         [(= mid-pos pos) mid]
+         [(mid-pos . > . pos) (loop lo-pos lo mid)]
+         [else (loop (+ lo-pos len) mid hi)])])))
+
 ;; For functions like `regexp-match/end`:
 (define (add-end-bytes results end-bytes-count bstr me-pos)
   (if end-bytes-count
diff --git a/racket/src/regexp/match/main.rkt b/racket/src/regexp/match/main.rkt
index 2d1ed2290d..56315f4a83 100644
--- a/racket/src/regexp/match/main.rkt
+++ b/racket/src/regexp/match/main.rkt
@@ -236,7 +236,7 @@
            (byte-positions->byte-positions ms-pos me-pos state #:delta delta)]
           [else
            (byte-positions->string-positions bstr-in ms-pos me-pos state
-                                              #:start-offset start-offset)]))
+                                             #:result-offset start-offset)]))
        (add-end-bytes positions end-bytes-count bstr-in me-pos)]
       [(strings)
        ;; If pattern is bytes-based, then results will be bytes instead of strings:
@@ -343,9 +343,18 @@
             (define delta (- start-offset start-pos))
             (byte-positions->byte-positions ms-pos me-pos state #:delta delta)]
            [else
+            ;; Some bytes may have been discarded in `lb-in`, and we
+            ;; don't know how many characters those add up to. The
+            ;; starting position `ms-pos` must be on a code-point
+            ;; boundary, and everything from `ms-pos` to `ms-end` must
+            ;; still be in `lb-in`. So, find `ms-pos` in the original
+            ;; string, and take it from there.
+            (define ms-str-pos (byte-index->string-index in (- ms-pos start-pos)))
+            (define delta (lazy-bytes-discarded-count lb-in))
             (byte-positions->string-positions bstr ms-pos me-pos state
-                                              #:start-pos start-pos
-                                              #:start-offset start-offset)]))
+                                              #:start-index (- ms-pos delta)
+                                              #:delta delta
+                                              #:result-offset (+ ms-str-pos start-offset))]))
         (add-end-bytes positions end-bytes-count bstr me-pos)]
        [(strings)
         ;; The byte string may be shifted by discarded bytes, if not