diff --git a/homeassistant/components/template/cover.py b/homeassistant/components/template/cover.py
index d985473792e..a9f28d56669 100644
--- a/homeassistant/components/template/cover.py
+++ b/homeassistant/components/template/cover.py
@@ -62,8 +62,7 @@ POSITION_ACTION = "set_cover_position"
 TILT_ACTION = "set_cover_tilt_position"
 CONF_TILT_OPTIMISTIC = "tilt_optimistic"
 
-CONF_VALUE_OR_POSITION_TEMPLATE = "value_or_position"
-CONF_OPEN_OR_CLOSE = "open_or_close"
+CONF_OPEN_AND_CLOSE = "open_or_close"
 
 TILT_FEATURES = (
     SUPPORT_OPEN_TILT
@@ -76,15 +75,10 @@ COVER_SCHEMA = vol.All(
     cv.deprecated(CONF_ENTITY_ID),
     vol.Schema(
         {
-            vol.Inclusive(OPEN_ACTION, CONF_OPEN_OR_CLOSE): cv.SCRIPT_SCHEMA,
-            vol.Inclusive(CLOSE_ACTION, CONF_OPEN_OR_CLOSE): cv.SCRIPT_SCHEMA,
+            vol.Inclusive(OPEN_ACTION, CONF_OPEN_AND_CLOSE): cv.SCRIPT_SCHEMA,
+            vol.Inclusive(CLOSE_ACTION, CONF_OPEN_AND_CLOSE): cv.SCRIPT_SCHEMA,
             vol.Optional(STOP_ACTION): cv.SCRIPT_SCHEMA,
-            vol.Exclusive(
-                CONF_POSITION_TEMPLATE, CONF_VALUE_OR_POSITION_TEMPLATE
-            ): cv.template,
-            vol.Exclusive(
-                CONF_VALUE_TEMPLATE, CONF_VALUE_OR_POSITION_TEMPLATE
-            ): cv.template,
+            vol.Optional(CONF_VALUE_TEMPLATE): cv.template,
             vol.Optional(CONF_AVAILABILITY_TEMPLATE): cv.template,
             vol.Optional(CONF_POSITION_TEMPLATE): cv.template,
             vol.Optional(CONF_TILT_TEMPLATE): cv.template,
@@ -258,10 +252,11 @@ class CoverTemplate(TemplateEntity, CoverEntity):
         state = str(result).lower()
 
         if state in _VALID_STATES:
-            if state in ("true", STATE_OPEN):
-                self._position = 100
-            else:
-                self._position = 0
+            if not self._position_template:
+                if state in ("true", STATE_OPEN):
+                    self._position = 100
+                else:
+                    self._position = 0
 
             self._is_opening = state == STATE_OPENING
             self._is_closing = state == STATE_CLOSING
@@ -271,7 +266,8 @@ class CoverTemplate(TemplateEntity, CoverEntity):
                 state,
                 ", ".join(_VALID_STATES),
             )
-            self._position = None
+            if not self._position_template:
+                self._position = None
 
     @callback
     def _update_position(self, result):
diff --git a/tests/components/template/test_cover.py b/tests/components/template/test_cover.py
index c1309a16e67..e2b65abcf25 100644
--- a/tests/components/template/test_cover.py
+++ b/tests/components/template/test_cover.py
@@ -34,7 +34,7 @@ def calls_fixture(hass):
     return async_mock_service(hass, "test", "automation")
 
 
-async def test_template_state_text(hass, calls):
+async def test_template_state_text(hass, calls, caplog):
     """Test the state text of a template."""
     with assert_setup_component(1, "cover"):
         assert await setup.async_setup_component(
@@ -64,30 +64,147 @@ async def test_template_state_text(hass, calls):
     await hass.async_start()
     await hass.async_block_till_done()
 
-    state = hass.states.async_set("cover.test_state", STATE_OPEN)
+    hass.states.async_set("cover.test_state", STATE_OPEN)
     await hass.async_block_till_done()
-
     state = hass.states.get("cover.test_template_cover")
     assert state.state == STATE_OPEN
 
-    state = hass.states.async_set("cover.test_state", STATE_CLOSED)
+    hass.states.async_set("cover.test_state", STATE_CLOSED)
     await hass.async_block_till_done()
-
     state = hass.states.get("cover.test_template_cover")
     assert state.state == STATE_CLOSED
 
-    state = hass.states.async_set("cover.test_state", STATE_OPENING)
+    hass.states.async_set("cover.test_state", STATE_OPENING)
     await hass.async_block_till_done()
-
     state = hass.states.get("cover.test_template_cover")
     assert state.state == STATE_OPENING
 
-    state = hass.states.async_set("cover.test_state", STATE_CLOSING)
+    hass.states.async_set("cover.test_state", STATE_CLOSING)
     await hass.async_block_till_done()
-
     state = hass.states.get("cover.test_template_cover")
     assert state.state == STATE_CLOSING
 
+    # Unknown state sets position to None - "closing" takes precedence
+    state = hass.states.async_set("cover.test_state", "dog")
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_CLOSING
+    assert "Received invalid cover is_on state: dog" in caplog.text
+
+    # Set state to open
+    hass.states.async_set("cover.test_state", STATE_OPEN)
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPEN
+
+    # Unknown state sets position to None -> Open
+    state = hass.states.async_set("cover.test_state", "cat")
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPEN
+    assert "Received invalid cover is_on state: cat" in caplog.text
+
+    # Set state to closed
+    hass.states.async_set("cover.test_state", STATE_CLOSED)
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_CLOSED
+
+    # Unknown state sets position to None -> Open
+    state = hass.states.async_set("cover.test_state", "bear")
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPEN
+    assert "Received invalid cover is_on state: bear" in caplog.text
+
+
+async def test_template_state_text_combined(hass, calls, caplog):
+    """Test the state text of a template which combines position and value templates."""
+    with assert_setup_component(1, "cover"):
+        assert await setup.async_setup_component(
+            hass,
+            "cover",
+            {
+                "cover": {
+                    "platform": "template",
+                    "covers": {
+                        "test_template_cover": {
+                            "position_template": "{{ states.cover.test.attributes.position }}",
+                            "value_template": "{{ states.cover.test_state.state }}",
+                            "open_cover": {
+                                "service": "cover.open_cover",
+                                "entity_id": "cover.test_state",
+                            },
+                            "close_cover": {
+                                "service": "cover.close_cover",
+                                "entity_id": "cover.test_state",
+                            },
+                        }
+                    },
+                }
+            },
+        )
+
+    await hass.async_block_till_done()
+    await hass.async_start()
+    await hass.async_block_till_done()
+
+    # Test default state
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPEN
+
+    # Change to "open" should be ignored
+    state = hass.states.async_set("cover.test_state", STATE_OPEN)
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPEN
+
+    # Change to "closed" should be ignored
+    state = hass.states.async_set("cover.test_state", STATE_CLOSED)
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPEN
+
+    # Change to "opening" should be accepted
+    state = hass.states.async_set("cover.test_state", STATE_OPENING)
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPENING
+
+    # Change to "closing" should be accepted
+    state = hass.states.async_set("cover.test_state", STATE_CLOSING)
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_CLOSING
+
+    # Set position to 0=closed
+    hass.states.async_set("cover.test", STATE_CLOSED, attributes={"position": 0})
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_CLOSING
+    assert state.attributes["current_position"] == 0
+
+    # Clear "closing" state, STATE_OPEN will be ignored and state derived from position
+    state = hass.states.async_set("cover.test_state", STATE_OPEN)
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_CLOSED
+
+    # Set position to 10
+    hass.states.async_set("cover.test", STATE_CLOSED, attributes={"position": 10})
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPEN
+    assert state.attributes["current_position"] == 10
+
+    # Unknown state should be ignored
+    state = hass.states.async_set("cover.test_state", "dog")
+    await hass.async_block_till_done()
+    state = hass.states.get("cover.test_template_cover")
+    assert state.state == STATE_OPEN
+    assert state.attributes["current_position"] == 10
+    assert "Received invalid cover is_on state: dog" in caplog.text
+
 
 async def test_template_state_boolean(hass, calls):
     """Test the value_template attribute."""
@@ -250,43 +367,6 @@ async def test_template_out_of_bounds(hass, calls):
     assert state.attributes.get("current_position") is None
 
 
-async def test_template_mutex(hass, calls):
-    """Test that only value or position template can be used."""
-    with assert_setup_component(0, "cover"):
-        assert await setup.async_setup_component(
-            hass,
-            "cover",
-            {
-                "cover": {
-                    "platform": "template",
-                    "covers": {
-                        "test_template_cover": {
-                            "value_template": "{{ 1 == 1 }}",
-                            "position_template": "{{ 42 }}",
-                            "open_cover": {
-                                "service": "cover.open_cover",
-                                "entity_id": "cover.test_state",
-                            },
-                            "close_cover": {
-                                "service": "cover.close_cover",
-                                "entity_id": "cover.test_state",
-                            },
-                            "icon_template": "{% if states.cover.test_state.state %}"
-                            "mdi:check"
-                            "{% endif %}",
-                        }
-                    },
-                }
-            },
-        )
-
-    await hass.async_block_till_done()
-    await hass.async_start()
-    await hass.async_block_till_done()
-
-    assert hass.states.async_all() == []
-
-
 async def test_template_open_or_position(hass, caplog):
     """Test that at least one of open_cover or set_position is used."""
     assert await setup.async_setup_component(