diff --git a/glymur/jp2k.py b/glymur/jp2k.py
index 9623abc..bd90dfe 100644
--- a/glymur/jp2k.py
+++ b/glymur/jp2k.py
@@ -636,10 +636,18 @@ class Jp2k(Jp2kBox):
         """
         self._subsampling_sanity_check()
 
-        if rlevel == -1:
-            # Get the lowest resolution thumbnail.
+        if rlevel != 0:
+            # Must check the specified rlevel against the maximum.
+            # OpenJPEG 1.3 will segfault if rlevel is too high.
             codestream = self.get_codestream()
-            rlevel = codestream.segment[2].spcod[4]
+            max_rlevel = codestream.segment[2].spcod[4]
+            if rlevel == -1:
+                # -1 is shorthand for the largest rlevel
+                rlevel = max_rlevel
+            if rlevel < -1 or rlevel > max_rlevel:
+                msg = "rlevel must be in the range [-1, {0}] for this image."
+                msg = msg.format(max_rlevel)
+                raise IOError(msg)
 
         with ExitStack() as stack:
             # Set decoding parameters.
diff --git a/glymur/test/test_jp2k.py b/glymur/test/test_jp2k.py
index 2ca5d9b..ea19199 100644
--- a/glymur/test/test_jp2k.py
+++ b/glymur/test/test_jp2k.py
@@ -817,7 +817,7 @@ class TestJp2k15(unittest.TestCase):
     def test_rlevel_too_high(self):
         """Should error out appropriately if reduce level too high"""
         j = Jp2k(self.jp2file)
-        with self.assertRaises(ValueError):
+        with self.assertRaises(IOError):
             j.read(rlevel=6)
 
     def test_not_jpeg2000(self):