diff --git a/tests/rules/common.py b/tests/rules/common.py
index 0d31550..cf5ff07 100644
--- a/tests/rules/common.py
+++ b/tests/rules/common.py
@@ -37,8 +37,15 @@ class RuleTestCase(unittest.TestCase):
         expected_problems = []
         for key in kwargs:
             assert key.startswith('problem')
+            if len(kwargs[key]) > 2:
+                if kwargs[key][2] == 'syntax':
+                    rule_id = None
+                else:
+                    rule_id = kwargs[key][2]
+            else:
+                rule_id = self.rule_id
             expected_problems.append(
-                LintProblem(kwargs[key][0], kwargs[key][1], rule=self.rule_id))
+                LintProblem(kwargs[key][0], kwargs[key][1], rule=rule_id))
         expected_problems.sort()
 
         real_problems = list(lint(source, self.build_fake_config(conf)))
diff --git a/tests/rules/test_document_start.py b/tests/rules/test_document_start.py
index 29a6dc0..b19dc8f 100644
--- a/tests/rules/test_document_start.py
+++ b/tests/rules/test_document_start.py
@@ -82,7 +82,7 @@ class DocumentStartTestCase(RuleTestCase):
                    '...\n'
                    'second: document\n'
                    '---\n'
-                   'third: document\n', conf, problem=(4, 1))
+                   'third: document\n', conf, problem=(4, 1, 'syntax'))
 
     def test_directives(self):
         conf = 'document-start: {present: yes}'
diff --git a/tests/rules/test_indentation.py b/tests/rules/test_indentation.py
index cdebdf7..e71fdc9 100644
--- a/tests/rules/test_indentation.py
+++ b/tests/rules/test_indentation.py
@@ -163,7 +163,7 @@ class IndentationTestCase(RuleTestCase):
         self.check('---\n'
                    '- o:\n'
                    ' k1: v1\n'
-                   '...\n', conf, problem=(3, 2))
+                   '...\n', conf, problem=(3, 2, 'syntax'))
         self.check('---\n'
                    '- o:\n'
                    '   k1: v1\n'
@@ -192,18 +192,18 @@ class IndentationTestCase(RuleTestCase):
                    '      f:\n'
                    'g:\n'
                    '...\n', None)
-        # self.check('---\n'
-        #            'a:\n'
-        #            '  b:\n'
-        #            '    c:\n'
-        #            '   d:\n'
-        #            '...\n', None, problem=(5, 5))
-        # self.check('---\n'
-        #            'a:\n'
-        #            '  b:\n'
-        #            '    c:\n'
-        #            ' d:\n'
-        #            '...\n', None, problem=(5, 2))
+        self.check('---\n'
+                   'a:\n'
+                   '  b:\n'
+                   '    c:\n'
+                   '   d:\n'
+                   '...\n', None, problem=(5, 4, 'syntax'))
+        self.check('---\n'
+                   'a:\n'
+                   '  b:\n'
+                   '    c:\n'
+                   ' d:\n'
+                   '...\n', None, problem=(5, 2, 'syntax'))
 
     def test_first_line(self):
         conf = ('indentation: {spaces: 2}\n'
diff --git a/tests/rules/test_trailing_spaces.py b/tests/rules/test_trailing_spaces.py
index 75ffe3d..9bbfbfd 100644
--- a/tests/rules/test_trailing_spaces.py
+++ b/tests/rules/test_trailing_spaces.py
@@ -33,11 +33,11 @@ class TrailingSpacesTestCase(RuleTestCase):
         self.check('', conf)
         self.check('\n', conf)
         self.check('    \n', conf, problem=(1, 1))
-        self.check('\t\t\t\n', conf, problem=(1, 1))
+        self.check('\t\t\t\n', conf, problem=(1, 1, 'syntax'))
         self.check('---\n'
                    'some: text \n', conf, problem=(2, 11))
         self.check('---\n'
-                   'some: text\t\n', conf, problem=(2, 11))
+                   'some: text\t\n', conf, problem=(2, 11, 'syntax'))
 
     def test_with_dos_new_lines(self):
         conf = ('trailing-spaces: {}\n'
diff --git a/yamllint/__init__.py b/yamllint/__init__.py
index 4595133..1bb1a54 100644
--- a/yamllint/__init__.py
+++ b/yamllint/__init__.py
@@ -81,15 +81,16 @@ def _lint(buffer, conf):
         # Insert the syntax error (if any) at the right place...
         if (syntax_error and syntax_error.line <= problem.line and
                 syntax_error.column <= problem.column):
-            # ... unless there is already a yamllint error at the same place,
-            # in which case the syntax error is probably redundant.
-            # In such a case, the yamllint problem is preferred, except if its
-            # level is not 'error' (because the script needs to exit with a
-            # failure status, the syntax error is preferred here).
-            if (syntax_error.line != problem.line or
-                    syntax_error.column != problem.column or
-                    problem.level != 'error'):
-                yield syntax_error
+            yield syntax_error
+
+            # If there is already a yamllint error at the same place, discard
+            # it as it is probably redundant (and maybe it's just a 'warning',
+            # in which case the script won't even exit with a failure status).
+            if (syntax_error.line == problem.line and
+                    syntax_error.column == problem.column):
+                syntax_error = None
+                continue
+
             syntax_error = None
 
         yield problem