diff --git a/collects/net/unihead.rkt b/collects/net/unihead.rkt
index 1cc821c1c1..7dd39246d8 100644
--- a/collects/net/unihead.rkt
+++ b/collects/net/unihead.rkt
@@ -10,37 +10,68 @@
         [(not (regexp-match? #rx"\r\n" s)) (encode-line-for-header s)] ; speed
         [else (regexp-replace* #rx"[^\r\n]+" s encode-line-for-header)]))
 
+;; Note: the following two encoder wrappers remove newlines from the
+;; encoded strings.  This avoids producing invalid strings, but it's not
+;; complete: rfc2047 (section 2) specifies that encoded words should not
+;; be longer than 75 characters, and longer words should be split for
+;; encoding with a separator of CRLF SPACE between them.  The problem is
+;; that doing this properly requires changing the encoders to get a
+;; length limit and have them return also the leftover unencoded string.
+;; Instead of doing all of that, do something simpler: if the string to
+;; be encoded is longer than 70 characters, then split it.  (This is
+;; done in `encode-line-for-header' below.)  It's possible to get longer
+;; encodings with this, but it seems that sendmail's limit on line
+;; lengths is sufficiently larger that it works fine in practice.  (BTW,
+;; when sendmail gets lines that are too long it splits them with the
+;; dreaded "!\n ", and it looks like there is no sane way to avoid that
+;; behavior -- so splitting the input is needed.)
+
+(define (base64-encode-header s)
+  (regexp-replace* #rx#"[\r\n]+" (base64-encode s) #""))
+
+(define (qp-encode-header s)
+  ;; rfc2047 (section 4.2) calls this "Q encoding", which is different
+  ;; from the usual QP encoding: encode underlines and question marks,
+  ;; and replace spaces by underlines; also remove soft-newlines.
+  (regexp-replace* #rx#"[ ?_]"
+                   (regexp-replace* #rx#"=\r?\n" (qp-encode s) #"")
+                   (λ (b)
+                     (case (bytes-ref b 0)
+                       [(32) #"_"]   ; " "
+                       [(63) #"=3F"] ; "?"
+                       [(95) #"=5F"] ; "_"
+                       [else (error 'qp-encode-header "internal error")]))))
+
 (define (encode-line-for-header s)
-  (define (loop s string->bytes charset encode encoding)
-    ;; Find ASCII (and no "=") prefix before a space
-    (let ([m (regexp-match #rx"^([\u0-\u3c\u3e-\u7F]* )(.*)$" s)])
-      (if m
-        (string-append
-         (cadr m)
-         (loop (caddr m) string->bytes charset encode encoding))
+  (define (do-encode s string->bytes charset encode encoding)
+    (let loop ([s s])
+      (cond
+        ;; Find ASCII (and no "=") prefix before a space
+        [(regexp-match #rx"^([\u0-\u3c\u3e-\u7F]* )(.*)$" s)
+         => (λ (m) (string-append (cadr m) (loop (caddr m))))]
         ;; Find ASCII (and no "=") suffix after a space
-        (let ([m (regexp-match #rx"^(.*?)( [\u0-\u3c\u3e-\u7F]*)$" s)])
-          (if m
-            (string-append
-             (loop (cadr m) string->bytes charset encode encoding)
-             (caddr m))
-            (format "=?~a?~a?~a?="
-                    charset encoding
-                    (regexp-replace* #rx#"[\r\n]+$"
-                                     (encode (string->bytes s))
-                                     #"")))))))
+        [(regexp-match #rx"^(.*?)( [\u0-\u3c\u3e-\u7F]*)$" s)
+         => (λ (m) (string-append (loop (cadr m)) (caddr m)))]
+        [else
+         ;; Split lines longer than 70 chars and re-assemble (see above
+         ;; comment).  Note that the proper separator should use CRLF,
+         ;; but we're sending this to a sendmail process that will take
+         ;; care of that level.
+         (let loop ([bytes (string->bytes s)])
+           (if ((bytes-length bytes) . > . 70)
+             (string-append (loop (subbytes bytes 0 70))
+                            "\n "
+                            (loop (subbytes bytes 70)))
+             (format "=?~a?~a?~a?=" charset encoding (encode bytes))))])))
   (cond
     ;; ASCII - do nothing
     [(not (regexp-match? re:non-ascii s)) s]
     ;; Not Latin-1, so use UTF-8
     [(regexp-match? #rx"[^\u0-\uFF]" s)
-     (loop s string->bytes/utf-8 "UTF-8" base64-encode "B")]
+     (do-encode s string->bytes/utf-8 "UTF-8" base64-encode-header "B")]
     ;; use Latin-1
     [else
-     (loop s string->bytes/latin-1 "ISO-8859-1"
-           (lambda (s)
-             (regexp-replace #rx#" " (qp-encode s) #"_"))
-           "Q")]))
+     (do-encode s string->bytes/latin-1 "ISO-8859-1" qp-encode-header "Q")]))
 
 ;; ----------------------------------------
 
@@ -65,8 +96,7 @@
          (if m
            (let ([s ((if (member (cadddr m) '(#"q" #"Q"))
                        ;; quoted-printable, with special _ handling
-                       (lambda (x)
-                         (qp-decode (regexp-replace* #rx#"_" x #" ")))
+                       (λ (x) (qp-decode (regexp-replace* #rx#"_" x #" ")))
                        ;; base64:
                        base64-decode)
                      (cadddr (cdr m)))]