diff --git a/lisp/emacs-lisp/package.el b/lisp/emacs-lisp/package.el
index 4268f7d27a7..d619142d64c 100644
--- a/lisp/emacs-lisp/package.el
+++ b/lisp/emacs-lisp/package.el
@@ -930,7 +930,7 @@ untar into a directory named DIR; otherwise, signal an error."
         (or (string-match regexp name)
             ;; Tarballs created by some utilities don't list
             ;; directories with a trailing slash (Bug#13136).
-            (and (string-equal dir name)
+            (and (string-equal (expand-file-name dir) name)
                  (eq (tar-header-link-type tar-data) 5))
             (error "Package does not untar cleanly into directory %s/" dir)))))
   (tar-untar-buffer))
@@ -1192,8 +1192,12 @@ Return the pkg-desc, with desc-kind set to KIND."
   "Find package information for a tar file.
 The return result is a `package-desc'."
   (cl-assert (derived-mode-p 'tar-mode))
-  (let* ((dir-name (file-name-directory
-                    (tar-header-name (car tar-parse-info))))
+  (let* ((dir-name (named-let loop
+                       ((filename (tar-header-name (car tar-parse-info))))
+                     (let ((dirname (file-name-directory filename)))
+                       ;; The first file can be in a subdir: look for the top.
+                       (if dirname (loop (directory-file-name dirname))
+                         (file-name-as-directory filename)))))
          (desc-file (package--description-file dir-name))
          (tar-desc (tar-get-file-descriptor (concat dir-name desc-file))))
     (unless tar-desc
diff --git a/test/lisp/emacs-lisp/package-resources/ustar-withsub-0.1.tar b/test/lisp/emacs-lisp/package-resources/ustar-withsub-0.1.tar
new file mode 100644
index 00000000000..009c4fc420c
Binary files /dev/null and b/test/lisp/emacs-lisp/package-resources/ustar-withsub-0.1.tar differ
diff --git a/test/lisp/emacs-lisp/package-resources/v7-withsub-0.1.tar b/test/lisp/emacs-lisp/package-resources/v7-withsub-0.1.tar
new file mode 100644
index 00000000000..16c79e529f4
Binary files /dev/null and b/test/lisp/emacs-lisp/package-resources/v7-withsub-0.1.tar differ
diff --git a/test/lisp/emacs-lisp/package-tests.el b/test/lisp/emacs-lisp/package-tests.el
index b903cd781ba..ffe4d7cd5fd 100644
--- a/test/lisp/emacs-lisp/package-tests.el
+++ b/test/lisp/emacs-lisp/package-tests.el
@@ -275,11 +275,31 @@ Must called from within a `tar-mode' buffer."
 
     (let* ((pkg-el "multi-file-0.2.3.tar")
            (source-file (expand-file-name pkg-el (ert-resource-directory))))
-      (package-initialize)
       (should-not (package-installed-p 'multie-file))
       (package-install-file source-file)
       (should (package-installed-p 'multi-file))
-      (package-delete (cadr (assq 'multi-file package-alist))))
+      (package-delete (cadr (assq 'multi-file package-alist))))))
+
+(ert-deftest package-test-bug58367 ()
+  "Check variations in tarball formats."
+  (with-package-test (:basedir (ert-resource-directory))
+    (package-initialize)
+
+    ;; A package whose first entry is the main dir but without trailing /.
+    (let* ((pkg-el "ustar-withsub-0.1.tar")
+           (source-file (expand-file-name pkg-el (ert-resource-directory))))
+      (should-not (package-installed-p 'ustar-withsub))
+      (package-install-file source-file)
+      (should (package-installed-p 'ustar-withsub))
+      (package-delete (cadr (assq 'ustar-withsub package-alist))))
+
+    ;; A package whose first entry is a file in a subdir.
+    (let* ((pkg-el "v7-withsub-0.1.tar")
+           (source-file (expand-file-name pkg-el (ert-resource-directory))))
+      (should-not (package-installed-p 'v7-withsub))
+      (package-install-file source-file)
+      (should (package-installed-p 'v7-withsub))
+      (package-delete (cadr (assq 'v7-withsub package-alist))))
     ))
 
 (ert-deftest package-test-install-file-EOLs ()