diff --git a/lisp/emacs-lisp/cl-generic.el b/lisp/emacs-lisp/cl-generic.el
index 8de45626bf0..4c6c6a0007c 100644
--- a/lisp/emacs-lisp/cl-generic.el
+++ b/lisp/emacs-lisp/cl-generic.el
@@ -1442,6 +1442,7 @@ Used internally for the (major-mode MODE) context specializers."
    (cl-call-next-method)))
 
 (cl--generic-prefill-dispatchers 0 oclosure)
+(cl--generic-prefill-dispatchers 0 (eql 'x) oclosure integer)
 
 ;;; Support for unloading.
 
diff --git a/lisp/frameset.el b/lisp/frameset.el
index 1796d2af072..9de16750c44 100644
--- a/lisp/frameset.el
+++ b/lisp/frameset.el
@@ -1444,6 +1444,11 @@ Called from `list-registers' and `view-register'.  Internal use only."
 		   (if (= 1 ns) "" "s")
 		   (format-time-string "%c" (frameset-timestamp fs))))))
 
+(cl-defmethod register--type ((_regval frameset-register))
+  ;; FIXME: Why `frame' rather than `frameset'?
+  ;; FIXME: We shouldn't need to touch an internal function.
+  'frame)
+
 ;;;###autoload
 (defun frameset-to-register (register)
   "Store the current frameset in register REGISTER.
diff --git a/lisp/register.el b/lisp/register.el
index ad2abf7e4ea..cdb769991f4 100644
--- a/lisp/register.el
+++ b/lisp/register.el
@@ -35,7 +35,6 @@
 
 ;; FIXME: Clean up namespace usage!
 
-(declare-function frameset-register-p "frameset")
 (declare-function dired-current-directory "dired")
 
 (cl-defstruct
@@ -64,6 +63,7 @@ They both receive DATA as argument."
   (registerv--make data print-func jump-func insert-func))
 
 (defvar register-alist nil
+  ;; FIXME: This conflates the FRAME-CONFIGURATION and the FRAMESET cases.
   "Alist of elements (NAME . CONTENTS), one for each Emacs register.
 NAME is a character (a number).  CONTENTS is a string, number, marker, list
 or a struct returned by `registerv-make'.
@@ -387,10 +387,7 @@ satisfy `cl-typep', otherwise the new type should be defined with
 (cl-defmethod register--type ((_regval (eql file))) 'file)
 (cl-defmethod register--type ((_regval (eql file-query))) 'file-query)
 (cl-defmethod register--type ((_regval window-configuration)) 'window)
-(cl-deftype frame-register () '(satisfies frameset-register-p))
-(cl-defmethod register--type :extra "frame-register" (_regval) 'frame)
-(cl-deftype kmacro-register () '(satisfies kmacro-register-p))
-(cl-defmethod register--type :extra "kmacro-register" (_regval) 'kmacro)
+(cl-defmethod register--type ((regval oclosure)) (oclosure-type regval))
 
 (defun register-of-type-alist (types)
   "Filter `register-alist' according to TYPES."
@@ -644,6 +641,8 @@ Interactively, prompt for REGISTER using `register-read-with-preview'."
   ;; Turn the marker into a file-ref if the buffer is killed.
   (add-hook 'kill-buffer-hook 'register-swap-out nil t)
   (set-register register
+                ;; FIXME: How does this `current-frame-configuration' differ
+                ;; in practice with what `frameset-to-register' does?
 		(if arg (list (current-frame-configuration) (point-marker))
 		  (point-marker))))