diff --git a/setup.py b/setup.py
index 31010c2..70f7be7 100644
--- a/setup.py
+++ b/setup.py
@@ -8,7 +8,7 @@
 
 setup(
     name="pyvalem",
-    version="2.5.15",
+    version="2.5.16",
     description="A package for managing simple chemical species and states",
     long_description=long_description,
     long_description_content_type="text/x-rst",
diff --git a/src/pyvalem/states/racah_symbol.py b/src/pyvalem/states/racah_symbol.py
index c7cdcab..0db7315 100644
--- a/src/pyvalem/states/racah_symbol.py
+++ b/src/pyvalem/states/racah_symbol.py
@@ -13,6 +13,7 @@
 
 orbital_labels = ("s", "s'", "p", "p'", "d", "d'", "f", "f'")
 atom_orbital = pp.oneOf(orbital_labels).setResultsName("orbital")
+parity_label = pp.Literal("o").setResultsName("parity")
 
 atom_k_term = (
     integer.setResultsName("k_num") + pp.Suppress("/") + integer.setResultsName("k_den")
@@ -25,8 +26,9 @@
     + atom_orbital
     + pp.Suppress("[")
     + atom_k_term
-    + pp.Suppress("]_")
-    + atom_j_term
+    + pp.Suppress("]")
+    + pp.Optional(parity_label)
+    + pp.Optional("_" + atom_j_term)
 )
 
 
@@ -36,7 +38,8 @@ class RacahSymbol(State):
 
     This class is currently little more than a stub. The term symbol of the
     parent configuration must be specified as a separate State; this class
-    defines nl[K]_J, without the parity label ("superscript-o").
+    defines nl[K]_J, where _J is optional to allow for the case where a
+    state is an average over J levels.
     """
 
     def __init__(self, state_str):
@@ -47,6 +50,7 @@ def __init__(self, state_str):
         self.k_num = None
         self.k_den = None
         self.j_term = None
+        self.parity = None
         self._parse_state(state_str)
 
     def _parse_state(self, state_str):
@@ -62,15 +66,20 @@ def _parse_state(self, state_str):
             self.parent_rot = 1.5
         self.k_num = int(components.k_num)
         self.k_den = int(components.k_den)
-        self.j_term = int(components.jterm)
+        self.parity = "o" if components.parity else ""
+        if components.jterm != "":
+            self.j_term = int(components.jterm)
 
     def __repr__(self):
-        parent = "{}{}".format(self.principal, self.orbital)
-        k = "{}/{}".format(self.k_num, self.k_den)
-        return "{}[{}]_{}".format(parent, k, self.j_term)
+        parent = f"{self.principal}{self.orbital}"
+        k = f"{self.k_num}/{self.k_den}"
+        s_jterm = f"_{self.j_term}" if self.j_term is not None else ""
+        return f"{parent}[{k}]{self.parity}{s_jterm}"
 
     @property
     def html(self):
-        parent = "{}{}".format(self.principal, self.orbital)
-        k = "{}/{}".format(self.k_num, self.k_den)
-        return "{}[{}]<sub>{}</sub>".format(parent, k, self.j_term)
+        parent = f"{self.principal}{self.orbital}"
+        k = f"{self.k_num}/{self.k_den}"
+        s_parity = "<sup>o</sup>" if self.parity else ""
+        s_jterm = f"<sub>{self.j_term}</sub>" if self.j_term is not None else ""
+        return f"{parent}[{k}]{s_parity}{s_jterm}"
diff --git a/tests/test_racah_symbols.py b/tests/test_racah_symbols.py
index cc73bc7..2659db9 100644
--- a/tests/test_racah_symbols.py
+++ b/tests/test_racah_symbols.py
@@ -18,6 +18,7 @@ def test_racah_symbol(self):
         self.assertEqual(r0.j_term, 1)
 
         r1 = RacahSymbol("3p[5/2]_2")
+        self.assertEqual(repr(r1), "3p[5/2]_2")
         self.assertEqual(r1.html, "3p[5/2]<sub>2</sub>")
         self.assertEqual(r1.principal, 3)
         self.assertEqual(r1.orbital, "p")
@@ -25,6 +26,26 @@ def test_racah_symbol(self):
         self.assertEqual(r1.k_den, 2)
         self.assertEqual(r1.j_term, 2)
 
+        r2 = RacahSymbol("4d[3/2]")
+        self.assertEqual(repr(r2), "4d[3/2]")
+        self.assertEqual(r2.html, "4d[3/2]")
+        self.assertEqual(r2.principal, 4)
+        self.assertEqual(r2.orbital, "d")
+        self.assertEqual(r2.k_num, 3)
+        self.assertEqual(r2.k_den, 2)
+        self.assertEqual(r2.j_term, None)
+        self.assertEqual(r2.parity, "")
+
+        r3 = RacahSymbol("3p[3/2]o_2")
+        self.assertEqual(repr(r3), "3p[3/2]o_2")
+        self.assertEqual(r3.html, "3p[3/2]<sup>o</sup><sub>2</sub>")
+        self.assertEqual(r3.principal, 3)
+        self.assertEqual(r3.orbital, "p")
+        self.assertEqual(r3.k_num, 3)
+        self.assertEqual(r3.k_den, 2)
+        self.assertEqual(r3.j_term, 2)
+        self.assertEqual(r3.parity, "o")
+
 
 if __name__ == "__main__":
     unittest.main()