Which surely can't be optimal?  If modified as follows, the duplicated
text disappears:

diff --git a/lisp/calc/calc.el b/lisp/calc/calc.el
index bf8b006d7c..62c0bea6d4 100644
--- a/lisp/calc/calc.el
+++ b/lisp/calc/calc.el
@@ -1396,8 +1396,6 @@ calc--header-line
         (let* ((len-long (length long))
                (len-short (length short))
                (fudge (or fudge 0))
-               ;; fudge for trail is: -3 (added to len-long)
-               ;; (width  ) for trail
                (factor (if (> width (+ len-long fudge)) len-long len-short))
                (size   (max (/ (- width factor) 2) 0))
                (fill (make-string size ?-))
@@ -1428,6 +1426,12 @@ calc-create-buffer
   (set-buffer (get-buffer-create "*Calculator*"))
   (or (derived-mode-p 'calc-mode)
       (calc-mode))
+  (when calc-show-banner
+    (calc--header-line "Emacs Calculator Mode" "Emacs Calc"
+                       (if calc-display-trail
+                           (/ (* (window-width) 2) 3)
+                         (window-width))
+                       1))
   (setq max-lisp-eval-depth (max max-lisp-eval-depth 1000))
   (when calc-always-load-extensions
     (require 'calc-ext))
@@ -2009,8 +2013,8 @@ calc-refresh
 	 (setq calc-any-selections nil)
 	 (erase-buffer)
          (when calc-show-banner
-           (calc--header-line  "Emacs Calculator Mode" "Emacs Calc"
-                       (* 2 (/ (window-width) 3)) -3))
+           (calc--header-line "Emacs Calculator Mode" "Emacs Calc"
+                              (window-width) 1))
 	 (while thing
 	   (goto-char (point-min))
 	   (insert (math-format-stack-value (car thing)) "\n")
@@ -2133,29 +2137,32 @@ calc-record
 (defun calc-trail-display (flag &optional no-refresh interactive)
   (interactive "P\ni\np")
   (let ((win (get-buffer-window (calc-trail-buffer))))
-    (if (setq calc-display-trail
-	      (not (if flag (memq flag '(nil 0)) win)))
-	(if (null win)
-	    (progn
-              (if calc-trail-window-hook
-                  (run-hooks 'calc-trail-window-hook)
-                (let ((w (split-window nil (/ (* (window-width) 2) 3) t)))
-                  (set-window-buffer w calc-trail-buffer)))
-              (calc-wrapper
-               (setq overlay-arrow-string calc-trail-overlay
-                     overlay-arrow-position calc-trail-pointer)
-               (or no-refresh
-                   (if interactive
-                       (calc-do-refresh)
-                     (calc-refresh))))))
-      (if win
-	  (progn
-	    (delete-window win)
-	    (calc-wrapper
-	     (or no-refresh
-		 (if interactive
-		     (calc-do-refresh)
-		   (calc-refresh))))))))
+    (cond
+     ((setq calc-display-trail
+	    (not (if flag (memq flag '(nil 0)) win)))
+      (when (null win)
+        (if calc-trail-window-hook
+            (run-hooks 'calc-trail-window-hook)
+          (setq win (split-window nil (/ (* (window-width) 2) 3) t))
+          (set-window-buffer win calc-trail-buffer))
+        (calc-wrapper
+         (setq overlay-arrow-string calc-trail-overlay
+               overlay-arrow-position calc-trail-pointer)
+         (or no-refresh
+             (if interactive
+                 (calc-do-refresh)
+               (calc-refresh)))))
+      (with-current-buffer calc-trail-buffer
+        (when calc-show-banner
+          (calc--header-line "Emacs Calculator Trail" "Calc Trail"
+                             (window-width win) -3))))
+     (win                               ; not calc-display-trail
+      (delete-window win)
+      (calc-wrapper
+       (or no-refresh
+	   (if interactive
+	       (calc-do-refresh)
+             (calc-refresh)))))))
   calc-trail-buffer)
 
 (defun calc-trail-here ()


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