diff --git a/backend/webdav/webdav.go b/backend/webdav/webdav.go
index 206b11bd1..397cd0b92 100644
--- a/backend/webdav/webdav.go
+++ b/backend/webdav/webdav.go
@@ -1068,6 +1068,13 @@ func (f *Fs) copyOrMove(ctx context.Context, src fs.Object, remote string, metho
 	if err != nil {
 		return nil, fmt.Errorf("copy NewObject failed: %w", err)
 	}
+	if f.useOCMtime && resp.Header.Get("X-OC-Mtime") != "accepted" && f.propsetMtime {
+		fs.Debugf(dstObj, "Setting modtime after copy to %v", src.ModTime(ctx))
+		err = dstObj.SetModTime(ctx, src.ModTime(ctx))
+		if err != nil {
+			return nil, fmt.Errorf("failed to set modtime: %w", err)
+		}
+	}
 	return dstObj, nil
 }
 
diff --git a/fstest/test_all/config.yaml b/fstest/test_all/config.yaml
index 413ed60d1..89a2bd46b 100644
--- a/fstest/test_all/config.yaml
+++ b/fstest/test_all/config.yaml
@@ -333,10 +333,6 @@ backends:
    ignore:
      - TestIntegration/FsMkdir/FsEncoding/punctuation
      - TestIntegration/FsMkdir/FsEncoding/invalid_UTF-8
-     - TestIntegration/FsMkdir/FsPutFiles/FsCopy
-     - TestCopyFileCopyDest
-     - TestServerSideCopy
-     - TestSyncCopyDest
    fastlist: false
  - backend:  "webdav"
    remote:   "TestWebdavRclone:"