diff --git a/doc/source/v0.14.1.txt b/doc/source/v0.14.1.txt
index 3160b35386fa2..7a9b9ddaf19f4 100644
--- a/doc/source/v0.14.1.txt
+++ b/doc/source/v0.14.1.txt
@@ -136,6 +136,9 @@ Enhancements
 
 - ``Period`` and ``PeriodIndex`` can contain ``NaT`` in its values (:issue:`7485`)
 
+- ``read_csv`` and ``read_table`` can now read index columns from the first
+  line after the header when using the C engine (:issue:`6893`)
+
 
 .. _whatsnew_0141.performance:
 
diff --git a/pandas/io/parsers.py b/pandas/io/parsers.py
index 22fe3ef16e34d..12e5820953b2e 100644
--- a/pandas/io/parsers.py
+++ b/pandas/io/parsers.py
@@ -1079,6 +1079,10 @@ def __init__(self, src, **kwds):
 
         self.orig_names = self.names
 
+        # index_col may be specified on line after the header
+        if self.index_col is None:
+            self.index_col = self._reader.index_col
+
         if not self._has_complex_date_col:
             if (self._reader.leading_cols == 0 and
                     _is_index_col(self.index_col)):
diff --git a/pandas/io/tests/test_parsers.py b/pandas/io/tests/test_parsers.py
index c02a3172f4adc..cc7d844cedd32 100644
--- a/pandas/io/tests/test_parsers.py
+++ b/pandas/io/tests/test_parsers.py
@@ -1568,21 +1568,22 @@ def test_converter_return_string_bug(self):
         self.assertEqual(df2['Number1'].dtype, float)
 
     def test_read_table_buglet_4x_multiindex(self):
-        # GH 6607
-        # Parsing multi-level index currently causes an error in the C parser.
-        # Temporarily copied to TestPythonParser.
-        # Here test that CParserError is raised:
-
-        with tm.assertRaises(CParserError):
-            text = """                      A       B       C       D        E
+        text = """                      A       B       C       D        E
 one two three   four
 a   b   10.0032 5    -0.5109 -2.3358 -0.4645  0.05076  0.3640
 a   q   20      4     0.4473  1.4152  0.2834  1.00661  0.1744
 x   q   30      3    -0.6662 -0.5243 -0.3580  0.89145  2.5838"""
 
-            # it works!
-            df = self.read_table(StringIO(text), sep='\s+')
-            self.assertEqual(df.index.names, ('one', 'two', 'three', 'four'))
+        # it works!
+        df = self.read_table(StringIO(text), sep='\s+')
+        self.assertEqual(df.index.names, ('one', 'two', 'three', 'four'))
+
+        # GH 6893
+        data = '      A B C\na b c\n1 3 7 0 3 6\n3 1 4 1 5 9'
+        expected = DataFrame.from_records([(1,3,7,0,3,6), (3,1,4,1,5,9)],
+                columns=list('abcABC'), index=list('abc'))
+        actual = self.read_table(StringIO(data), sep='\s+')
+        tm.assert_frame_equal(actual, expected)
 
     def test_read_csv_parse_simple_list(self):
         text = """foo
@@ -2713,28 +2714,6 @@ def test_decompression_regex_sep(self):
             self.assertRaises(ValueError, self.read_csv,
                               path, compression='bz3')
 
-    def test_read_table_buglet_4x_multiindex(self):
-        # GH 6607
-        # This is a copy which should eventually be merged into ParserTests
-        # when the issue with multi-level index is fixed in the C parser.
-
-        text = """                      A       B       C       D        E
-one two three   four
-a   b   10.0032 5    -0.5109 -2.3358 -0.4645  0.05076  0.3640
-a   q   20      4     0.4473  1.4152  0.2834  1.00661  0.1744
-x   q   30      3    -0.6662 -0.5243 -0.3580  0.89145  2.5838"""
-
-        # it works!
-        df = self.read_table(StringIO(text), sep='\s+')
-        self.assertEqual(df.index.names, ('one', 'two', 'three', 'four'))
-
-        # GH 6893
-        data = '      A B C\na b c\n1 3 7 0 3 6\n3 1 4 1 5 9'
-        expected = DataFrame.from_records([(1,3,7,0,3,6), (3,1,4,1,5,9)],
-                columns=list('abcABC'), index=list('abc'))
-        actual = self.read_table(StringIO(data), sep='\s+')
-        tm.assert_frame_equal(actual, expected)
-
 class TestFwfColspaceSniffing(tm.TestCase):
     def test_full_file(self):
         # File with all values
diff --git a/pandas/parser.pyx b/pandas/parser.pyx
index f303298e88273..8e80862cb19fb 100644
--- a/pandas/parser.pyx
+++ b/pandas/parser.pyx
@@ -574,6 +574,17 @@ cdef class TextReader:
             raise IOError('Expected file path name or file-like object,'
                           ' got %s type' % type(source))
 
+    cdef _word2name(self, word, char *errors):
+        if self.c_encoding == NULL and not PY3:
+            name = PyBytes_FromString(word)
+        else:
+            if self.c_encoding == NULL or self.c_encoding == b'utf-8':
+                name = PyUnicode_FromString(word)
+            else:
+                name = PyUnicode_Decode(word, strlen(word),
+                                        self.c_encoding, errors)
+        return name
+
     cdef _get_header(self):
         # header is now a list of lists, so field_count should use header[0]
 
@@ -612,16 +623,7 @@ cdef class TextReader:
                 counts = {}
                 unnamed_count = 0
                 for i in range(field_count):
-                    word = self.parser.words[start + i]
-
-                    if self.c_encoding == NULL and not PY3:
-                        name = PyBytes_FromString(word)
-                    else:
-                        if self.c_encoding == NULL or self.c_encoding == b'utf-8':
-                            name = PyUnicode_FromString(word)
-                        else:
-                            name = PyUnicode_Decode(word, strlen(word),
-                                                    self.c_encoding, errors)
+                    name = self._word2name(self.parser.words[start + i], errors)
 
                     if name == '':
                         if self.has_mi_columns:
@@ -685,13 +687,56 @@ cdef class TextReader:
         else: # not self.has_usecols:
 
             field_count = self.parser.line_fields[data_line]
+            passed_count = len(header[0])
+
+            # #6893: look for index columns on first line after header
+
+            # hack: temporarily set expected_fields to prevent parser from
+            # raising if it sees extra columns
+            ex_fields = self.parser.expected_fields
+            self.parser.expected_fields = field_count
+
+            datapos = self.parser.datapos   # save position
+            self._tokenize_rows(1)
+            self.parser.expected_fields = ex_fields # restore expected_fields
+
+            if self.parser.lines == data_line + 2:
+                field_count_next = self.parser.line_fields[data_line + 1]
+
+                if field_count_next > field_count:
+                    # found extra columns in the second row after the header
+                    # check whether previous row contains index columns
+                    start = self.parser.line_start[data_line]
+
+                    line = [self._word2name(self.parser.words[start + i], errors)
+                            for i in range(self.parser.line_fields[data_line])]
+
+                    # remove trailing empty fields
+                    while not line[-1]:
+                        line.pop()
+
+                    if passed_count + len(line) == field_count_next:
+                        for h in header:
+                            for c in reversed(line):
+                                h.insert(0, c)
+
+                        field_count = field_count_next
+                        passed_count = field_count
+                        self.index_col = line
+                        self.parser_start += 1
+
+                    else:
+                        # hack: didn't find index columns, back up a line and
+                        # let the parser code hande this...
+                        self.parser.datapos = datapos
+                        self.parser.lines -= 1
+                        self.parser.file_lines -= 1
+                        self.parser.line_fields[self.parser.lines] = 0
 
             # #2981
             if self.names is not None:
                 field_count = max(field_count, len(self.names))
 
-            passed_count = len(header[0])
-
             # if passed_count > field_count:
             #     raise CParserError('Column names have %d fields, '
             #                        'data has %d fields'