diff --git a/esmvalcore/_recipe/check.py b/esmvalcore/_recipe/check.py
index 55e1b52709..ea528c71f8 100644
--- a/esmvalcore/_recipe/check.py
+++ b/esmvalcore/_recipe/check.py
@@ -239,8 +239,9 @@ def data_availability(dataset: Dataset, log: bool = True) -> None:
         msg = f"Missing data for {dataset.summary(True)}"
         raise InputFilesNotFound(msg)
 
-    if "timerange" not in facets or any(
-        "timerange" not in f.facets for f in input_files
+    if (
+        "*" in facets.get("timerange", "*")  # type: ignore[operator]
+        or any("timerange" not in f.facets for f in input_files)
     ):
         return
 
diff --git a/esmvalcore/dataset.py b/esmvalcore/dataset.py
index 5c799d0843..3d1083b331 100644
--- a/esmvalcore/dataset.py
+++ b/esmvalcore/dataset.py
@@ -230,10 +230,6 @@ def _get_available_datasets(self) -> Iterator[Dataset]:
         """
         dataset_template = self.copy()
         dataset_template.supplementaries = []
-        if _isglob(dataset_template.facets.get("timerange")):
-            # Remove wildcard `timerange` facet, because data finding cannot
-            # handle it
-            dataset_template.facets.pop("timerange")
 
         seen = set()
         partially_defined = []
@@ -960,6 +956,7 @@ def _update_timerange(self) -> None:
         dataset.supplementaries = []
         dataset.augment_facets()
         if "timerange" not in dataset.facets:
+            # timerange facet may be removed in augment_facets for time-independent data.
             self.facets.pop("timerange", None)
             return
 
diff --git a/esmvalcore/local.py b/esmvalcore/local.py
index bb0b2049f1..e8d63abcc7 100644
--- a/esmvalcore/local.py
+++ b/esmvalcore/local.py
@@ -594,7 +594,7 @@ def find_data(self, **facets: FacetValue) -> list[LocalFile]:
                 file.facets.update(
                     self._path2facets(
                         file,
-                        add_timerange="timerange" in facets,
+                        add_timerange=facets.get("frequency", "fx") != "fx",
                     ),
                 )
                 file.ignore_warnings = self.ignore_warnings
diff --git a/tests/integration/dataset/test_dataset.py b/tests/integration/dataset/test_dataset.py
index 8558e1de28..5bbb7e22d3 100644
--- a/tests/integration/dataset/test_dataset.py
+++ b/tests/integration/dataset/test_dataset.py
@@ -61,6 +61,33 @@ def example_data_source(tmp_path: Path) -> dict[str, str]:
     }
 
 
+@pytest.mark.parametrize("timerange", ["1850/185002", "*", "*/P2M", "1860/*"])
+def test_find_data(
+    example_data_source: dict[str, str],
+    session: Session,
+    timerange: str,
+) -> None:
+    tas = Dataset(
+        short_name="tas",
+        mip="Amon",
+        project="CMIP5",
+        dataset="CanESM2",
+        ensemble="r1i1p1",
+        exp="historical",
+        timerange=timerange,
+    )
+    tas.add_supplementary(short_name="areacella", mip="fx", ensemble="r0i0p0")
+    tas.session = session
+    tas.session["projects"]["CMIP5"]["data"] = {
+        "example-data-source": example_data_source,
+    }
+
+    assert len(tas.files) == 1
+    assert "timerange" in tas.files[0].facets
+    assert len(tas.supplementaries[0].files) == 1
+    assert "timerange" not in tas.supplementaries[0].files
+
+
 def test_load(example_data_source: dict[str, str], session: Session) -> None:
     tas = Dataset(
         short_name="tas",