diff --git a/Annex/CopyFile.hs b/Annex/CopyFile.hs
index b49f2ef45b..b4ed97dfd5 100644
--- a/Annex/CopyFile.hs
+++ b/Annex/CopyFile.hs
@@ -15,6 +15,8 @@ import Utility.CopyFile
 import Utility.FileMode
 import Utility.Touch
 import Utility.Hash (IncrementalVerifier(..))
+import Annex.Tmp
+import Utility.Tmp
 
 import Control.Concurrent
 import qualified Data.ByteString as S
@@ -28,23 +30,34 @@ newCopyCoWTried :: IO CopyCoWTried
 newCopyCoWTried = CopyCoWTried <$> newEmptyMVar
 
 {- Copies a file is copy-on-write is supported. Otherwise, returns False. -}
-tryCopyCoW :: CopyCoWTried -> FilePath -> FilePath -> MeterUpdate -> IO Bool
+tryCopyCoW :: CopyCoWTried -> FilePath -> FilePath -> MeterUpdate -> Annex Bool
 tryCopyCoW (CopyCoWTried copycowtried) src dest meterupdate =
 	-- If multiple threads reach this at the same time, they
 	-- will both try CoW, which is acceptable.
-	ifM (isEmptyMVar copycowtried)
+	ifM (liftIO $ isEmptyMVar copycowtried)
 		( do
 			ok <- docopycow
-			void $ tryPutMVar copycowtried ok
+			void $ liftIO $ tryPutMVar copycowtried ok
 			return ok
-		, ifM (readMVar copycowtried)
+		, ifM (liftIO $ readMVar copycowtried)
 			( docopycow
 			, return False
 			)
 		)
   where
-	docopycow = watchFileSize dest meterupdate $
-		copyCoW CopyTimeStamps src dest
+	-- copyCow needs a destination file that does not exist,
+	-- but the dest file might already. So use it with another
+	-- temp file, and if it succeeds, rename it into place. If it fails,
+	-- the dest file is left as-is, to support resuming.
+	docopycow = withOtherTmp $ \othertmp -> liftIO $
+		withTmpFileIn (fromRawFilePath othertmp) (takeFileName dest) $ \tmpdest _h -> do
+			copied <- watchFileSize tmpdest meterupdate $
+				copyCoW CopyTimeStamps src tmpdest
+			if copied
+				then liftIO $ catchBoolIO $ do
+					rename tmpdest dest
+					return True
+				else return False
 
 data CopyMethod = CopiedCoW | Copied
 
@@ -70,7 +83,7 @@ fileCopier :: CopyCoWTried -> FilePath -> FilePath -> MeterUpdate -> Maybe Incre
 fileCopier _ src dest meterupdate iv = docopy
 #else
 fileCopier copycowtried src dest meterupdate iv =
-	ifM (liftIO $ tryCopyCoW copycowtried src dest meterupdate)
+	ifM (tryCopyCoW copycowtried src dest meterupdate)
 		( do
 			liftIO $ maybe noop unableIncremental iv
 			return CopiedCoW
diff --git a/CHANGELOG b/CHANGELOG
index 538ae62a49..c1e6446bed 100644
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -2,6 +2,8 @@ git-annex (8.20210904) UNRELEASED; urgency=medium
 
   * borg: Avoid trying to extract xattrs, ACLS, and bsdflags when
     retrieving from a borg repository.
+  * Resume where it left off when copying a file to/from a local git remote
+    was interrupted.
 
  -- Joey Hess <id@joeyh.name>  Fri, 03 Sep 2021 12:02:55 -0400
 
diff --git a/Remote/Directory.hs b/Remote/Directory.hs
index 6a34df6bd0..20d4027323 100644
--- a/Remote/Directory.hs
+++ b/Remote/Directory.hs
@@ -412,7 +412,7 @@ retrieveExportWithContentIdentifierM dir cow loc cid dest mkkey p =
 	f = exportPath dir loc
 	f' = fromRawFilePath f
 
-	docopy = ifM (liftIO $ tryCopyCoW cow f' dest p)
+	docopy = ifM (tryCopyCoW cow f' dest p)
 		( do
 			k <- mkkey
 			postcheckcow (return k)
diff --git a/Utility/CopyFile.hs b/Utility/CopyFile.hs
index ed2da15e5c..e91986593a 100644
--- a/Utility/CopyFile.hs
+++ b/Utility/CopyFile.hs
@@ -56,11 +56,13 @@ copyFileExternal meta src dest = do
 		| otherwise = copyMetaDataParams meta
 
 {- When a filesystem supports CoW (and cp does), uses it to make
- - an efficient copy of a file. Otherwise, returns False. -}
+ - an efficient copy of a file. Otherwise, returns False.
+ -
+ - The dest file must not exist yet, or it will fail to make a CoW copy,
+ - and will return False. -}
 copyCoW :: CopyMetaData -> FilePath -> FilePath -> IO Bool
 copyCoW meta src dest
 	| BuildInfo.cp_reflink_supported = do
-		void $ tryIO $ removeFile dest
 		-- When CoW is not supported, cp will complain to stderr,
 		-- so have to discard its stderr.
 		ok <- catchBoolIO $ withNullHandle $ \nullh ->
diff --git a/doc/bugs/copy_--to_with_local_git_remote_does_not_resume.mdwn b/doc/bugs/copy_--to_with_local_git_remote_does_not_resume.mdwn
new file mode 100644
index 0000000000..7361200daf
--- /dev/null
+++ b/doc/bugs/copy_--to_with_local_git_remote_does_not_resume.mdwn
@@ -0,0 +1,21 @@
+A copy --to a local git remote that gets interrupted and is run again does
+not resume where it left off, but copies all the data again.
+
+This does not affect git remotes accessed over ssh.
+
+It's kind of hard to notice this, because normally a resume, has to read
+the src file and dest file, in order for incremental verification to
+get started. But it is somewhat slower to do that than it is to re-write
+the dest file from the start. And when annex.verify = false, it's a lot
+slower.
+
+Looks like it's due to copyCoW unlinking the dest file. Since the first
+file copy trues copyCoW to probe if that's supported, that happens.
+And when resuming an interrupted copy, that probe will generally happen
+with the file it was interrupted on.
+
+So, the solution seems like it would be to copyCoW to some other temp file,
+and if it succeeds, rename it to the dest.
+--[[Joey]]
+
+> [[fixed|done]] --[[Joey]]