diff --git a/Orange/widgets/data/owselectcolumns.py b/Orange/widgets/data/owselectcolumns.py
index 9e673d25719..8b54eaf3ef9 100644
--- a/Orange/widgets/data/owselectcolumns.py
+++ b/Orange/widgets/data/owselectcolumns.py
@@ -5,7 +5,7 @@
 from AnyQt.QtWidgets import QListView
 from AnyQt.QtCore import (
     Qt, QTimer, QSortFilterProxyModel, QItemSelection, QItemSelectionModel,
-    QMimeData
+    QMimeData, QAbstractItemModel
 )
 
 from Orange.widgets import gui, widget
@@ -411,12 +411,20 @@ def selected_rows(view):
             rows = [model.mapToSource(r) for r in rows]
         return [r.row() for r in rows]
 
-    def move_rows(self, view, rows, offset):
-        model = view.model()
-        newrows = [min(max(0, row + offset), len(model) - 1) for row in rows]
+    def move_rows(self, view: QListView, offset: int, roles=(Qt.EditRole,)):
+        rows = [idx.row() for idx in view.selectionModel().selectedRows()]
+        model = view.model()  # type: QAbstractItemModel
+        rowcount = model.rowCount()
+        newrows = [min(max(0, row + offset), rowcount - 1) for row in rows]
+
+        def itemData(index):
+            return {role: model.data(index, role) for role in roles}
 
         for row, newrow in sorted(zip(rows, newrows), reverse=offset > 0):
-            model[row], model[newrow] = model[newrow], model[row]
+            d1 = itemData(model.index(row, 0))
+            d2 = itemData(model.index(newrow, 0))
+            model.setItemData(model.index(row, 0), d2)
+            model.setItemData(model.index(newrow, 0), d1)
 
         selection = QItemSelection()
         for nrow in newrows:
@@ -427,13 +435,11 @@ def move_rows(self, view, rows, offset):
 
         self.commit()
 
-    def move_up(self, view):
-        selected = self.selected_rows(view)
-        self.move_rows(view, selected, -1)
+    def move_up(self, view: QListView):
+        self.move_rows(view, -1)
 
-    def move_down(self, view):
-        selected = self.selected_rows(view)
-        self.move_rows(view, selected, 1)
+    def move_down(self, view: QListView):
+        self.move_rows(view, 1)
 
     def move_selected(self, view):
         if self.selected_rows(view):
diff --git a/Orange/widgets/data/tests/test_owselectcolumns.py b/Orange/widgets/data/tests/test_owselectcolumns.py
index 718678035ed..d9d6aed277c 100644
--- a/Orange/widgets/data/tests/test_owselectcolumns.py
+++ b/Orange/widgets/data/tests/test_owselectcolumns.py
@@ -363,3 +363,26 @@ def _drag_enter_event(self, variables):
         mime.setProperty("_items", variables)
         return QDragEnterEvent(QPoint(0, 0), Qt.MoveAction, mime,
                                Qt.NoButton, Qt.NoModifier)
+
+    def test_move_rows(self):
+        data = Table("iris")[:5]
+        w = self.widget
+        self.send_signal(w.Inputs.data, data)
+        view = w.used_attrs_view
+        model = view.model()
+        selmodel = view.selectionModel()
+        midx = model.index(1, 0)
+        selmodel.select(midx, selmodel.ClearAndSelect)
+
+        w.move_up(view)
+        d1 = self.get_output(w.Outputs.data, w)
+        self.assertEqual(
+            d1.domain.attributes,
+            data.domain.attributes[:2][::-1] + data.domain.attributes[2:]
+        )
+        w.move_down(view)
+        d1 = self.get_output(w.Outputs.data, w)
+        self.assertEqual(
+            d1.domain.attributes,
+            data.domain.attributes
+        )