diff --git a/lisp/window.el b/lisp/window.el
index 1b8fe2b262..7b8ca87f6a 100644
--- a/lisp/window.el
+++ b/lisp/window.el
@@ -9382,14 +9382,17 @@ fit-frame-to-buffer-1
              ((numberp (nth 1 sizes)) (* (nth 1 sizes) line-height))
              (t (window-min-size window nil nil t))))
            (max-width
-            (min
-             (cond
-              ((numberp max-width) (* max-width char-width))
-              ((numberp (nth 2 sizes)) (* (nth 2 sizes) char-width))
-              (t parent-or-display-width))
-             ;; The following is the maximum width that fits into the
-             ;; left and right margins.
-             (max (- right-margin left-margin outer-minus-body-width))))
+            (let ((max-width
+                   (cond
+                    ((numberp max-width) (* max-width char-width))
+                    ((numberp (nth 2 sizes)) (* (nth 2 sizes) char-width))
+                    ((not (eq only 'vertically)) parent-or-display-width))))
+              (when (numberp max-width)
+                (min max-width
+                     ;; The following is the maximum width that fits
+                     ;; into the left and right margins.
+                     (max (- right-margin left-margin
+                             outer-minus-body-width))))))
            (min-width
             (cond
              ((numberp min-width) (* min-width char-width))