diff --git a/Annex/Concurrent.hs b/Annex/Concurrent.hs
index f341e21d0d..cb22b6a463 100644
--- a/Annex/Concurrent.hs
+++ b/Annex/Concurrent.hs
@@ -1,6 +1,6 @@
 {- git-annex concurrent state
  -
- - Copyright 2015-2020 Joey Hess <id@joeyh.name>
+ - Copyright 2015-2021 Joey Hess <id@joeyh.name>
  -
  - Licensed under the GNU AGPL version 3 or higher.
  -}
@@ -19,8 +19,10 @@ import Types.Concurrency
 import Types.CatFileHandles
 import Annex.CheckAttr
 import Annex.CheckIgnore
+import Utility.ThreadScheduler
 
 import qualified Data.Map as M
+import Control.Concurrent.Async
 
 setConcurrency :: ConcurrencySetting -> Annex ()
 setConcurrency (ConcurrencyCmdLine s) = setConcurrency' s ConcurrencyCmdLine
@@ -98,3 +100,23 @@ mergeState st = do
 		uncurry addCleanupAction
 	Annex.Queue.mergeFrom st'
 	changeState $ \s -> s { errcounter = errcounter s + errcounter st' }
+
+{- Display a message, only when the action runs for a long enough
+ - amount of time.
+ - 
+ - The action should not display any other messages, progress, etc;
+ - if it did there could be some scrambling of the display since the
+ - message display could happen at the same time as other output,
+ - or after it.
+ -}
+showSideActionAfter :: Microseconds -> String -> Annex a -> Annex a
+showSideActionAfter t m a = do
+	waiter <- liftIO $ async $ unboundDelay t
+	let display = liftIO (waitCatch waiter) >>= \case
+		Left _ -> return ()
+		Right _ -> showSideAction m
+	displayer <- liftIO . async =<< forkState display
+	let cleanup = do
+		liftIO $ cancel waiter
+		join (liftIO (wait displayer))
+	a `finally` cleanup
diff --git a/Annex/Init.hs b/Annex/Init.hs
index 124e28865b..4bd0955eaa 100644
--- a/Annex/Init.hs
+++ b/Annex/Init.hs
@@ -37,6 +37,7 @@ import Annex.UUID
 import Annex.WorkTree
 import Annex.Fixup
 import Annex.Path
+import Annex.Concurrent
 import Config
 import Config.Files
 import Config.Smudge
@@ -133,8 +134,8 @@ initialize' mversion = checkInitializeAllowed $ do
 		then configureSmudgeFilter
 		else deconfigureSmudgeFilter
 	unlessM isBareRepo $ do
-		showSideAction "scanning for annexed files"
-		scanAnnexedFiles
+		showSideActionAfter oneSecond "scanning for annexed files" $
+			scanAnnexedFiles
 		hookWrite postCheckoutHook
 		hookWrite postMergeHook
 	AdjustedBranch.checkAdjustedClone >>= \case
diff --git a/Utility/ThreadScheduler.hs b/Utility/ThreadScheduler.hs
index ef69ead81f..9ab94d911e 100644
--- a/Utility/ThreadScheduler.hs
+++ b/Utility/ThreadScheduler.hs
@@ -15,6 +15,7 @@ module Utility.ThreadScheduler (
 	threadDelaySeconds,
 	waitForTermination,
 	oneSecond,
+	unboundDelay,
 ) where
 
 import Control.Monad
diff --git a/doc/todo/init__58__do_not_bother_scanning_if_in_git-annex_branch/comment_2_2cbfb22e8f1d89d4f78ade565554cb1c._comment b/doc/todo/init__58__do_not_bother_scanning_if_in_git-annex_branch/comment_2_2cbfb22e8f1d89d4f78ade565554cb1c._comment
new file mode 100644
index 0000000000..0142d78551
--- /dev/null
+++ b/doc/todo/init__58__do_not_bother_scanning_if_in_git-annex_branch/comment_2_2cbfb22e8f1d89d4f78ade565554cb1c._comment
@@ -0,0 +1,9 @@
+[[!comment format=mdwn
+ username="joey"
+ subject="""comment 2"""
+ date="2021-06-04T17:14:42Z"
+ content="""
+Made the scanning message not be displayed unless it takes at least 1
+second. Of course, if some test suite is still looking at that message,
+it will break..
+"""]]