diff --git a/etuples/dispatch.py b/etuples/dispatch.py
index c17a93c..66f9504 100644
--- a/etuples/dispatch.py
+++ b/etuples/dispatch.py
@@ -7,18 +7,39 @@
 from .core import etuple, ExpressionTuple
 
 try:
-    from unification.core import _reify, _unify
+    from unification.core import _reify, _unify, isvar
 except ModuleNotFoundError:
     pass
 else:
 
     def _unify_ExpressionTuple(u, v, s):
-        return _unify(u._tuple, v._tuple, s)
+        return _unify(getattr(u, "_tuple", u), getattr(v, "_tuple", v), s)
 
     _unify.add((ExpressionTuple, ExpressionTuple, Mapping), _unify_ExpressionTuple)
+    _unify.add((tuple, ExpressionTuple, Mapping), _unify_ExpressionTuple)
+    _unify.add((ExpressionTuple, tuple, Mapping), _unify_ExpressionTuple)
 
     def _reify_ExpressionTuple(u, s):
-        return etuple(*_reify(u._tuple, s))
+        # The point of all this: we don't want to lose the expression
+        # tracking/caching information.
+        res = _reify(u._tuple, s)
+
+        res_same = tuple(
+            a == b for a, b in zip(u, res) if not isvar(a) and not isvar(b)
+        )
+
+        if len(res_same) == len(u) and all(res_same):
+            # Everything is equal and there are no logic variables
+            return u
+
+        if getattr(u, "_parent", None) and all(res_same):
+            # If we simply swapped-out logic variables, then we don't want to
+            # lose the parent etuple information.
+            res = etuple(*res)
+            res._parent = u._parent
+            return res
+
+        return etuple(*res)
 
     _reify.add((ExpressionTuple, Mapping), _reify_ExpressionTuple)
 
diff --git a/requirements.txt b/requirements.txt
index c6525e4..887d45b 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,5 +1,5 @@
 -e ./
-unification
+logical-unification
 ipython
 coveralls
 pydocstyle>=3.0.0
diff --git a/tests/test_dispatch.py b/tests/test_dispatch.py
index 4b77936..877bc3e 100644
--- a/tests/test_dispatch.py
+++ b/tests/test_dispatch.py
@@ -108,4 +108,45 @@ def test_unification():
     res = unify(etuple(add, 1, 2), cons(a_lv, b_lv), {})
     assert res == {a_lv: add, b_lv: etuple(1, 2)}
 
-    assert reify(cons(a_lv, b_lv), res) == etuple(add, 1, 2)
+    res = reify(cons(a_lv, b_lv), res)
+    assert isinstance(res, ExpressionTuple)
+    assert res == etuple(add, 1, 2)
+
+    et = etuple(a_lv,)
+    res = reify(et, {a_lv: 1})
+    assert isinstance(res, ExpressionTuple)
+
+    et = etuple(a_lv,)
+    # We choose to allow unification with regular tuples.
+    if etuple(1) == (1,):
+        res = unify(et, (1,))
+        assert res == {a_lv: 1}
+
+    et = etuple(add, 1, 2)
+    assert et.eval_obj == 3
+
+    res = unify(et, cons(a_lv, b_lv))
+    assert res == {a_lv: add, b_lv: et[1:]}
+
+    # Make sure we've preserved the original object after deconstruction via
+    # `unify`
+    assert res[b_lv]._parent is et
+    assert ((res[a_lv],) + res[b_lv])._eval_obj == 3
+
+    # Make sure we've preserved the original object after reconstruction via
+    # `reify`
+    rf_res = reify(cons(a_lv, b_lv), res)
+    assert rf_res is et
+
+    et_lv = etuple(add, a_lv, 2)
+    assert reify(et_lv[1:], {})._parent is et_lv
+
+    # Reify a logic variable to another logic variable
+    assert reify(et_lv[1:], {a_lv: b_lv})._parent is et_lv
+
+    # TODO: We could propagate the parent etuple when a sub-etuple is `cons`ed
+    # with logic variables.
+    # et_1 = et[2:]
+    # et_2 = cons(b_lv, et_1)
+    # assert et_2._parent is et
+    # assert reify(et_2, {a_lv: 1})._parent is et