diff --git a/holonote/annotate/annotator.py b/holonote/annotate/annotator.py
index 527777c..d93a921 100644
--- a/holonote/annotate/annotator.py
+++ b/holonote/annotate/annotator.py
@@ -497,8 +497,6 @@ def selection_enabled(self) -> bool:
     @selection_enabled.setter
     def selection_enabled(self, enabled: bool) -> None:
         self._selection_enabled = enabled
-        if not enabled:
-            self.select_by_index()
 
     @property
     def editable_enabled(self) -> bool:
@@ -759,6 +757,9 @@ def __init__(self, spec: dict, **params):
             **params,
         )
 
+        self._selection_enabled = True
+        self._editable_enabled = True
+
     @classmethod
     def _infer_kdim_dtypes(self, element: hv.Element) -> dict:
         # Remove?
@@ -873,3 +874,24 @@ def revert_to_snapshot(self):
     def set_regions(self, **items):
         super().set_regions(**items)
         self.refresh()
+
+    @property
+    def selection_enabled(self) -> bool:
+        return self._selection_enabled
+
+    @selection_enabled.setter
+    def selection_enabled(self, enabled: bool) -> None:
+        for v in self._elements.values():
+            v.selection_enabled = enabled
+
+        if not enabled:
+            self.select_by_index()
+
+    @property
+    def editable_enabled(self) -> bool:
+        return self._editable_enabled
+
+    @editable_enabled.setter
+    def editable_enabled(self, enabled: bool) -> None:
+        for v in self._elements.values():
+            v.editable_enabled = enabled
diff --git a/holonote/tests/test_annotators_element.py b/holonote/tests/test_annotators_element.py
index 22a0325..262ab6f 100644
--- a/holonote/tests/test_annotators_element.py
+++ b/holonote/tests/test_annotators_element.py
@@ -143,3 +143,27 @@ def test_set_regions_multiple(multiple_annotators, element_range1d, element_rang
     output2 = output.iloc[0, 4]
     expected2 = "Test"
     assert output2 == expected2
+
+
+def test_editable_enabled(annotator_range1d, element_range1d):
+    annotator_range1d * element_range1d
+
+    annotator_range1d.editable_enabled = False
+    for element in annotator_range1d._elements.values():
+        assert not element.editable_enabled
+
+    annotator_range1d.editable_enabled = True
+    for element in annotator_range1d._elements.values():
+        assert element.editable_enabled
+
+
+def test_selection_enabled(annotator_range1d, element_range1d):
+    annotator_range1d * element_range1d
+
+    annotator_range1d.selection_enabled = False
+    for element in annotator_range1d._elements.values():
+        assert not element.selection_enabled
+
+    annotator_range1d.selection_enabled = True
+    for element in annotator_range1d._elements.values():
+        assert element.selection_enabled