diff --git a/gdb/dwarf2/cooked-index.c b/gdb/dwarf2/cooked-index.c
index 97a749f97e8..d5a21ee9dec 100644
--- a/gdb/dwarf2/cooked-index.c
+++ b/gdb/dwarf2/cooked-index.c
@@ -449,30 +449,22 @@ cooked_index_worker::start ()
 {
   gdb::thread_pool::g_thread_pool->post_task ([=] ()
   {
-    this->start_reading ();
+    try
+      {
+	do_reading ();
+      }
+    catch (const gdb_exception &exc)
+      {
+	m_failed = exc;
+	set (cooked_state::CACHE_DONE);
+      }
+
+    bfd_thread_cleanup ();
   });
 }
 
 /* See cooked-index.h.  */
 
-void
-cooked_index_worker::start_reading ()
-{
-  SCOPE_EXIT { bfd_thread_cleanup (); };
-
-  try
-    {
-      do_reading ();
-    }
-  catch (const gdb_exception &exc)
-    {
-      m_failed = exc;
-      set (cooked_state::CACHE_DONE);
-    }
-}
-
-/* See cooked-index.h.  */
-
 bool
 cooked_index_worker::wait (cooked_state desired_state, bool allow_quit)
 {
@@ -520,7 +512,7 @@ cooked_index_worker::wait (cooked_state desired_state, bool allow_quit)
 
   if (m_failed.has_value ())
     {
-      /* start_reading failed -- report it.  */
+      /* do_reading failed -- report it.  */
       exception_print (gdb_stderr, *m_failed);
       m_failed.reset ();
       return done;
diff --git a/gdb/dwarf2/cooked-index.h b/gdb/dwarf2/cooked-index.h
index f063fe088e8..86fbb8ffac4 100644
--- a/gdb/dwarf2/cooked-index.h
+++ b/gdb/dwarf2/cooked-index.h
@@ -534,13 +534,8 @@ protected:
   friend class cooked_index;
   void set (cooked_state desired_state);
 
-  /* Start reading DWARF.  This can be run in a worker thread without
-     problems.  */
-  void start_reading ();
-
-  /* Helper function that does most of the work for start_reading.
-     This must be able to be run in a worker thread without
-     problems.  */
+  /* Helper function that does the work of reading.  This must be able
+     to be run in a worker thread without problems.  */
   virtual void do_reading () = 0;
 
   /* A callback that can print stats, if needed.  This is called when
@@ -579,9 +574,9 @@ protected:
      arose during scanning have been reported by 'wait'.  This may
      only be modified on the main thread.  */
   bool m_reported = false;
-  /* If set, an exception occurred during start_reading; in this case
-     the scanning is stopped and this exception will later be reported
-     by the 'wait' method.  */
+  /* If set, an exception occurred during reading; in this case the
+     scanning is stopped and this exception will later be reported by
+     the 'wait' method.  */
   std::optional<gdb_exception> m_failed;
 };