diff --git a/lisp/progmodes/project.el b/lisp/progmodes/project.el
index 7a0bf1fdbf..2cad66e705 100644
--- a/lisp/progmodes/project.el
+++ b/lisp/progmodes/project.el
@@ -592,29 +592,12 @@ project-prefix-map
 
 ;;;###autoload (define-key ctl-x-map "p" project-prefix-map)
 
-;; We can't have these place-specific maps inherit from
-;; project-prefix-map because project--other-place-command needs to
-;; know which map the key binding came from, as if it came from one of
-;; these maps, we don't want to set display-buffer-overriding-action
-
-(defvar project-other-window-map
-  (let ((map (make-sparse-keymap)))
-    (define-key map "\C-o" #'project-display-buffer)
-    map)
-  "Keymap for project commands that display buffers in other windows.")
-
-(defvar project-other-frame-map
-  (let ((map (make-sparse-keymap)))
-    (define-key map "\C-o" #'project-display-buffer-other-frame)
-    map)
-  "Keymap for project commands that display buffers in other frames.")
-
-(defun project--other-place-command (action &optional map)
+(defun project--other-place-command (action)
   (let* ((key (read-key-sequence-vector nil t))
-         (place-cmd (lookup-key map key))
-         (generic-cmd (lookup-key project-prefix-map key))
-         (display-buffer-overriding-action (unless place-cmd action)))
-    (if-let ((cmd (or place-cmd generic-cmd)))
+         (cmd (lookup-key project-prefix-map key))
+         (display-buffer-overriding-action action)
+         (switch-to-buffer-obey-display-actions t))
+    (if cmd
         (call-interactively cmd)
       (user-error "%s is undefined" (key-description key)))))
 
@@ -628,8 +611,7 @@ project-other-window-command
 \\{project-other-window-map}"
   (interactive)
   (project--other-place-command '((display-buffer-pop-up-window)
-                                  (inhibit-same-window . t))
-                                project-other-window-map))
+                                  (inhibit-same-window . t))))
 
 ;;;###autoload (define-key ctl-x-4-map "p" #'project-other-window-command)
 
@@ -642,8 +624,7 @@ project-other-frame-command
 \\{project-prefix-map}
 \\{project-other-frame-map}"
   (interactive)
-  (project--other-place-command '((display-buffer-pop-up-frame))
-                                project-other-frame-map))
+  (project--other-place-command '((display-buffer-pop-up-frame))))
 
 ;;;###autoload (define-key ctl-x-5-map "p" #'project-other-frame-command)
 
@@ -971,31 +952,7 @@ project-switch-to-buffer
 project instances, as reported by `project-current' in each
 buffer, are identical."
   (interactive (list (project--read-project-buffer)))
-  (switch-to-buffer buffer))
-
-;;;###autoload
-(defun project-display-buffer (buffer-or-name)
-  "Display BUFFER-OR-NAME in some window, without selecting it.
-When called interactively, prompts for a buffer belonging to the
-current project.  Two buffers belong to the same project if their
-project instances, as reported by `project-current' in each
-buffer, are identical."
-  (interactive (list (project--read-project-buffer)))
-  (display-buffer buffer))
-
-;;;###autoload
-(defun project-display-buffer-other-frame (buffer-or-name)
-  "Display BUFFER-OR-NAME preferably in another frame.
-When called interactively, prompts for a buffer belonging to the
-current project.  Two buffers belong to the same project if their
-project instances, as reported by `project-current' in each
-buffer, are identical.
-
-This function uses `display-buffer-other-frame' as a subroutine,
-which see for how it is determined where the buffer will be
-displayed."
-  (interactive (list (project--read-project-buffer)))
-  (display-buffer-other-frame buffer))
+  (switch-to-buffer buffer-or-name))
 
 (defcustom project-kill-buffers-ignores
   '("\\*Help\\*")