diff --git a/datasette/renderer.py b/datasette/renderer.py
index 0e01f52f..4cb519b9 100644
--- a/datasette/renderer.py
+++ b/datasette/renderer.py
@@ -30,6 +30,10 @@ def convert_specific_columns_to_json(rows, columns, json_cols):
     return new_rows
 
 
+def _facet_without_infinites(facet):
+    return {**facet, "results": [remove_infinites(r) for r in facet["results"]]}
+
+
 def json_renderer(request, args, data, error, truncated=None):
     """Render a response as JSON"""
     status_code = 200
@@ -44,8 +48,23 @@ def json_renderer(request, args, data, error, truncated=None):
         )
 
     # unless _json_infinity=1 requested, replace infinity with None
-    if "rows" in data and not value_as_boolean(args.get("_json_infinity", "0")):
-        data["rows"] = [remove_infinites(row) for row in data["rows"]]
+    if not value_as_boolean(args.get("_json_infinity", "0")):
+        if "rows" in data:
+            data["rows"] = [remove_infinites(row) for row in data["rows"]]
+        # Facet values and labels can be infinities too
+        if isinstance(data.get("facet_results"), dict):
+            data["facet_results"] = {
+                **data["facet_results"],
+                "results": {
+                    name: _facet_without_infinites(facet)
+                    for name, facet in data["facet_results"]["results"].items()
+                },
+            }
+        if isinstance(data.get("sorted_facet_results"), list):
+            data["sorted_facet_results"] = [
+                _facet_without_infinites(facet)
+                for facet in data["sorted_facet_results"]
+            ]
 
     # Deal with the _shape option
     shape = args.get("_shape", "objects")
diff --git a/tests/test_table_api.py b/tests/test_table_api.py
index 58a5ddc3..840076ff 100644
--- a/tests/test_table_api.py
+++ b/tests/test_table_api.py
@@ -1290,6 +1290,40 @@ async def test_infinity_returned_as_null(ds_client):
     ]
 
 
+@pytest.mark.asyncio
+@pytest.mark.parametrize("extra", ("facet_results", "sorted_facet_results"))
+async def test_infinity_facet_values_returned_as_null(ds_client, extra):
+    # https://github.com/simonw/datasette/issues/2954
+    response = await ds_client.get(
+        "/fixtures/infinity.json?_facet=value&_extra=" + extra
+    )
+    assert response.status_code == 200
+
+    def reject_constant(token):
+        raise ValueError(f"Non-JSON numeric literal: {token}")
+
+    data = json.loads(response.text, parse_constant=reject_constant)
+    facets = data[extra]
+    facet = facets["results"]["value"] if extra == "facet_results" else facets[0]
+    values = sorted(
+        ((r["value"], r["label"]) for r in facet["results"]),
+        key=lambda pair: (pair[0] is not None, pair),
+    )
+    assert values == [(None, None), (None, None), (1.5, 1.5)]
+
+
+@pytest.mark.asyncio
+async def test_infinity_facet_values_returned_as_invalid_json_if_requested(ds_client):
+    response = await ds_client.get(
+        "/fixtures/infinity.json?_facet=value&_extra=facet_results&_json_infinity=1"
+    )
+    values = {
+        r["value"]
+        for r in response.json()["facet_results"]["results"]["value"]["results"]
+    }
+    assert values == {float("inf"), float("-inf"), 1.5}
+
+
 @pytest.mark.asyncio
 async def test_infinity_returned_as_invalid_json_if_requested(ds_client):
     response = await ds_client.get(