diff --git a/ibis/backends/sql/rewrites.py b/ibis/backends/sql/rewrites.py
index addc87ef7fea..551891798898 100644
--- a/ibis/backends/sql/rewrites.py
+++ b/ibis/backends/sql/rewrites.py
@@ -124,10 +124,15 @@ def filter_to_select(_, **kwargs):
     )
 
 
+def is_constant(value: ops.Value) -> bool:
+    return not value.relations and not value.find(ops.Impure, filter=ops.Value)
+
+
 @replace(p.Sort)
 def sort_to_select(_, **kwargs):
     """Convert a Sort node to a Select node."""
-    return Select(_.parent, selections=_.values, sort_keys=_.keys)
+    non_constant_keys = tuple(key for key in _.keys if not is_constant(key.expr))
+    return Select(_.parent, selections=_.values, sort_keys=non_constant_keys)
 
 
 @replace(p.Distinct)
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column/out.sql
index 28f406fe0583..f4810b5f65db 100644
--- a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column/out.sql
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column/out.sql
@@ -1,5 +1,6 @@
 SELECT
-  *
+  "t0"."f",
+  "t0"."c"
 FROM "star1" AS "t0"
 ORDER BY
   "t0"."f" ASC
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column_and_literal/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column_and_literal/out.sql
new file mode 100644
index 000000000000..f4810b5f65db
--- /dev/null
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column_and_literal/out.sql
@@ -0,0 +1,6 @@
+SELECT
+  "t0"."f",
+  "t0"."c"
+FROM "star1" AS "t0"
+ORDER BY
+  "t0"."f" ASC
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column_derived/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column_derived/out.sql
new file mode 100644
index 000000000000..1190c7bb4f4f
--- /dev/null
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/column_derived/out.sql
@@ -0,0 +1,6 @@
+SELECT
+  "t0"."f",
+  "t0"."c"
+FROM "star1" AS "t0"
+ORDER BY
+  "t0"."f" + 1 ASC
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/literal/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/literal/out.sql
new file mode 100644
index 000000000000..d622436bf0e7
--- /dev/null
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/literal/out.sql
@@ -0,0 +1,4 @@
+SELECT
+  "t0"."f",
+  "t0"."c"
+FROM "star1" AS "t0"
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/literal_derived/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/literal_derived/out.sql
new file mode 100644
index 000000000000..d622436bf0e7
--- /dev/null
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/literal_derived/out.sql
@@ -0,0 +1,4 @@
+SELECT
+  "t0"."f",
+  "t0"."c"
+FROM "star1" AS "t0"
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random/out.sql
index 3eba0f7b3f84..08d99827c8af 100644
--- a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random/out.sql
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random/out.sql
@@ -1,5 +1,16 @@
 SELECT
   *
-FROM "star1" AS "t0"
+FROM (
+  SELECT
+    "t1"."f",
+    "t1"."c"
+  FROM (
+    SELECT
+      *
+    FROM "star1" AS "t0"
+    ORDER BY
+      RANDOM() ASC
+  ) AS "t1"
+) AS "t2"
 ORDER BY
   RANDOM() ASC
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_and_column/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_and_column/out.sql
new file mode 100644
index 000000000000..e17a396e578a
--- /dev/null
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_and_column/out.sql
@@ -0,0 +1,18 @@
+SELECT
+  *
+FROM (
+  SELECT
+    "t1"."f",
+    "t1"."c"
+  FROM (
+    SELECT
+      *
+    FROM "star1" AS "t0"
+    ORDER BY
+      RANDOM() ASC,
+      "t0"."f" ASC
+  ) AS "t1"
+) AS "t2"
+ORDER BY
+  RANDOM() ASC,
+  "t2"."f" ASC
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_and_literal/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_and_literal/out.sql
new file mode 100644
index 000000000000..08d99827c8af
--- /dev/null
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_and_literal/out.sql
@@ -0,0 +1,16 @@
+SELECT
+  *
+FROM (
+  SELECT
+    "t1"."f",
+    "t1"."c"
+  FROM (
+    SELECT
+      *
+    FROM "star1" AS "t0"
+    ORDER BY
+      RANDOM() ASC
+  ) AS "t1"
+) AS "t2"
+ORDER BY
+  RANDOM() ASC
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_derived/out.sql b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_derived/out.sql
new file mode 100644
index 000000000000..6396ee29a4d7
--- /dev/null
+++ b/ibis/backends/tests/sql/snapshots/test_sql/test_order_by/random_derived/out.sql
@@ -0,0 +1,16 @@
+SELECT
+  *
+FROM (
+  SELECT
+    "t1"."f",
+    "t1"."c"
+  FROM (
+    SELECT
+      *
+    FROM "star1" AS "t0"
+    ORDER BY
+      RANDOM() + 1 ASC
+  ) AS "t1"
+) AS "t2"
+ORDER BY
+  RANDOM() + 1 ASC
\ No newline at end of file
diff --git a/ibis/backends/tests/sql/test_sql.py b/ibis/backends/tests/sql/test_sql.py
index f635da1c17a4..20a26320ffa5 100644
--- a/ibis/backends/tests/sql/test_sql.py
+++ b/ibis/backends/tests/sql/test_sql.py
@@ -266,11 +266,22 @@ def test_aggregate(star1, expr_fn, snapshot):
 
 @pytest.mark.parametrize(
     "key",
-    ["f", ibis.random()],
-    ids=["column", "random"],
+    [
+        pytest.param("f", id="column"),
+        pytest.param(ibis._.f + 1, id="column_derived"),
+        pytest.param(ibis.random(), id="random"),
+        pytest.param(ibis.random() + 1, id="random_derived"),
+        pytest.param(ibis.literal(5), id="literal"),
+        pytest.param(ibis.literal(5) + 1, id="literal_derived"),
+        pytest.param((ibis.random(), "f"), id="random_and_column"),
+        pytest.param((ibis.random(), ibis.literal(5)), id="random_and_literal"),
+        pytest.param(("f", ibis.literal(5)), id="column_and_literal"),
+    ],
 )
 def test_order_by(star1, key, snapshot):
-    expr = star1.order_by(key)
+    # We are doing two order_bys to test that the rewrite that drops constant keys
+    # works at all levels of the expression tree.
+    expr = star1.order_by(key).select("f", "c").order_by(key)
     snapshot.assert_match(to_sql(expr), "out.sql")