diff --git a/arrow/parser.py b/arrow/parser.py
index e4f368ad5..498f42854 100644
--- a/arrow/parser.py
+++ b/arrow/parser.py
@@ -109,6 +109,14 @@ def parse_iso(self, string):
             formats = [separator.join(self.MARKERS[:l-i])
                        for i in range(l)
                        for separator in self.SEPARATORS]
+            date_string = string
+
+        for separator in self.SEPARATORS:
+            date_components = date_string.split(separator)
+            if len(date_components) == 1:
+                continue
+            if date_components[len(date_components) - 1] > date_components[0]:
+                raise ParserError('Could not match input to any of {0} on \'{1}\''.format(formats, string))
 
         if has_time and has_tz:
             formats = [f + 'Z' for f in formats]
diff --git a/tests/parser_tests.py b/tests/parser_tests.py
index 7682df8c3..f59086837 100644
--- a/tests/parser_tests.py
+++ b/tests/parser_tests.py
@@ -236,6 +236,10 @@ def test_parse_subsecond(self):
         assertEqual(self.parser.parse('2013-01-01 12:30:45.987654', 'YYYY-MM-DD HH:mm:ss.SSSSSS'), expected)
         assertEqual(self.parser.parse_iso('2013-01-01 12:30:45.987654'), expected)
 
+    def test_parse_unsupported_iso(self):
+        with assertRaises(ParserError):
+            self.parser.parse_iso('03.04.2017')
+
     def test_parse_subsecond_rounding(self):
         expected = datetime(2013, 1, 1, 12, 30, 45, 987654)
         format = 'YYYY-MM-DD HH:mm:ss.S'