diff --git a/chess/syzygy.py b/chess/syzygy.py
index 6b326a5d1..91007191b 100644
--- a/chess/syzygy.py
+++ b/chess/syzygy.py
@@ -299,7 +299,7 @@ def filenames():
 
     for i in range(1, 6):
         for j in range(i, 6):
-            for k in range(j, 6):
+            for k in range(i, 6):
                 for l in range(j if i == k else k, 6):
                     yield "K%c%cvK%c%c" % (PCHR[i], PCHR[j], PCHR[k], PCHR[l])
 
diff --git a/test.py b/test.py
index b3e6f3079..3c26cecfe 100755
--- a/test.py
+++ b/test.py
@@ -1400,7 +1400,11 @@ def test_calc_key(self):
 
     def test_filenames(self):
         self.assertTrue("KPPvKN" in chess.syzygy.filenames())
-        self.assertTrue("KPPPvKN" in chess.syzygy.filenames())
+        self.assertTrue("KNNPvKN" in chess.syzygy.filenames())
+        self.assertTrue("KQRNvKR" in chess.syzygy.filenames())
+        self.assertTrue("KRRRvKR" in chess.syzygy.filenames())
+        self.assertTrue("KRRvKRR" in chess.syzygy.filenames())
+        self.assertTrue("KRNvKRP" in chess.syzygy.filenames())
 
     def test_probe_pawnless_wdl_table(self):
         wdl = chess.syzygy.WdlTable("data/syzygy", "KBNvK")