diff --git a/devito/types/basic.py b/devito/types/basic.py
index 348547d2b7..db455e8924 100644
--- a/devito/types/basic.py
+++ b/devito/types/basic.py
@@ -497,7 +497,7 @@ def _subs(self, old, new, **hints):
         devito subclasses of sympy types are quite strict.
         """
         try:
-            if old.name == self.name:
+            if old.is_Symbol and old.name == self.name:
                 return new
         except AttributeError:
             pass
diff --git a/tests/test_symbolics.py b/tests/test_symbolics.py
index 39e4bdfa68..e77adb0c26 100644
--- a/tests/test_symbolics.py
+++ b/tests/test_symbolics.py
@@ -375,6 +375,16 @@ def test_safeinv():
     assert 'SAFEINV' in str(op1)
     assert 'SAFEINV' in str(op2)
 
+    # Ensure .subs leaves the caller unchanged if no substitutions occur.
+    # We used to have a bug where passing SafeInv to .subs would result
+    # in the construction of weird, nonsensical objects due to the _subs
+    # stub in types.AbstractSymbol
+    f = Function(name='f', grid=grid)
+    ui = u1.indexify()
+    safeinv = SafeInv(ui, ui)
+    v = ui._subs(safeinv, f.indexify())
+    assert str(v) == 'u[x, y]'
+
 
 def test_def_function():
     foo0 = DefFunction('foo', arguments=['a', 'b'], template=['int'])