diff --git a/ibis/expr/operations/generic.py b/ibis/expr/operations/generic.py
index 754029e292b52..a33abd28bfae8 100644
--- a/ibis/expr/operations/generic.py
+++ b/ibis/expr/operations/generic.py
@@ -185,13 +185,7 @@ class Constant(Scalar, Singleton):
 
 @public
 class Impure(Value):
-    _counter = itertools.count()
-    uid: Optional[int] = None
-
-    def __init__(self, uid, **kwargs):
-        if uid is None:
-            uid = next(self._counter)
-        super().__init__(uid=uid, **kwargs)
+    pass
 
 
 @public
diff --git a/ibis/expr/operations/tests/test_generic.py b/ibis/expr/operations/tests/test_generic.py
index c7f4f17873db1..e0e5eb4c7a982 100644
--- a/ibis/expr/operations/tests/test_generic.py
+++ b/ibis/expr/operations/tests/test_generic.py
@@ -146,10 +146,6 @@ def test_NULL():
 
 
 @pytest.mark.parametrize("op", [ops.RandomScalar, ops.RandomUUID])
-def test_unique_impure_values(op):
-    assert op() != op()
-    assert hash(op()) != hash(op())
-
-    node = op()
-    other = node.copy()
-    assert node == other
+def test_impure_values_are_equal(op):
+    assert op() == op()
+    assert hash(op()) == hash(op())
diff --git a/ibis/expr/tests/test_newrels.py b/ibis/expr/tests/test_newrels.py
index 9635459d43144..276cd6607bb52 100644
--- a/ibis/expr/tests/test_newrels.py
+++ b/ibis/expr/tests/test_newrels.py
@@ -1618,7 +1618,7 @@ def test_impure_operation_dereferencing(func):
 
     expected = ops.Project(
         parent=t1,
-        values={"x": t1.x, "y": t1.y, "z": t1.y.cast("string")},
+        values={"x": t1.x, "y": t1.y, "z": impure.cast("string")},
     )
     assert t2.op() == expected
 
diff --git a/ibis/expr/types/relations.py b/ibis/expr/types/relations.py
index ee4c2003a85b0..d0e2d3889b954 100644
--- a/ibis/expr/types/relations.py
+++ b/ibis/expr/types/relations.py
@@ -169,7 +169,7 @@ def dereference_mapping(parents):
                 while isinstance(v, ops.Field) and v not in mapping:
                     mapping[v] = ops.Field(parent, k)
                     v = v.rel.values.get(v.name)
-            elif v not in mapping:
+            elif v not in mapping and not v.find(ops.Impure):
                 # do not dereference literal expressions
                 mapping[v] = ops.Field(parent, k)