diff --git a/.hgeol b/.hgeol
index aad79c21136..2919f76a110 100644
--- a/.hgeol
+++ b/.hgeol
@@ -38,6 +38,8 @@ Lib/test/xmltestdata/* = BIN
 
 Lib/venv/scripts/nt/* = BIN
 
+Lib/test/coding20731.py = BIN
+
 # All other files (which presumably are human-editable) are "native".
 # This must be the last rule!
 
diff --git a/Lib/test/coding20731.py b/Lib/test/coding20731.py
new file mode 100644
index 00000000000..b0e227ad110
--- /dev/null
+++ b/Lib/test/coding20731.py
@@ -0,0 +1,4 @@
+#coding:latin1
+
+
+
diff --git a/Lib/test/test_source_encoding.py b/Lib/test/test_source_encoding.py
index cd9d2b374c7..39b623e637f 100644
--- a/Lib/test/test_source_encoding.py
+++ b/Lib/test/test_source_encoding.py
@@ -5,6 +5,7 @@ from test.support import TESTFN, unlink, unload
 import importlib
 import os
 import sys
+import subprocess
 
 class SourceEncodingTest(unittest.TestCase):
 
@@ -58,6 +59,14 @@ class SourceEncodingTest(unittest.TestCase):
         # two bytes in common with the UTF-8 BOM
         self.assertRaises(SyntaxError, eval, b'\xef\xbb\x20')
 
+    def test_20731(self):
+        sub = subprocess.Popen([sys.executable, 
+                        os.path.join(os.path.dirname(__file__),
+                                     'coding20731.py')],
+                        stderr=subprocess.PIPE)
+        err = sub.communicate()[1]
+        self.assertEquals(err, b'')
+
     def test_error_message(self):
         compile(b'# -*- coding: iso-8859-15 -*-\n', 'dummy', 'exec')
         compile(b'\xef\xbb\xbf\n', 'dummy', 'exec')
diff --git a/Misc/NEWS b/Misc/NEWS
index 3604a307a9e..c63054a1a72 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -8,6 +8,9 @@ What's New in Python 3.4.1?
 Core and Builtins
 -----------------
 
+- Issue #20731: Properly position in source code files even if they
+  are opened in text mode. Patch by Serhiy Storchaka.
+
 - Issue #20637: Key-sharing now also works for instance dictionaries of
   subclasses.  Patch by Peter Ingebretson.
 
diff --git a/Parser/tokenizer.c b/Parser/tokenizer.c
index c32a3bfd1c8..7283058fc88 100644
--- a/Parser/tokenizer.c
+++ b/Parser/tokenizer.c
@@ -498,9 +498,13 @@ fp_setreadl(struct tok_state *tok, const char* enc)
 
     fd = fileno(tok->fp);
     /* Due to buffering the file offset for fd can be different from the file
-     * position of tok->fp. */
+     * position of tok->fp.  If tok->fp was opened in text mode on Windows,
+     * its file position counts CRLF as one char and can't be directly mapped
+     * to the file offset for fd.  Instead we step back one byte and read to
+     * the end of line.*/
     pos = ftell(tok->fp);
-    if (pos == -1 || lseek(fd, (off_t)pos, SEEK_SET) == (off_t)-1) {
+    if (pos == -1 ||
+        lseek(fd, (off_t)(pos > 0 ? pos - 1 : pos), SEEK_SET) == (off_t)-1) {
         PyErr_SetFromErrnoWithFilename(PyExc_OSError, NULL);
         goto cleanup;
     }
@@ -513,6 +517,12 @@ fp_setreadl(struct tok_state *tok, const char* enc)
     Py_XDECREF(tok->decoding_readline);
     readline = _PyObject_GetAttrId(stream, &PyId_readline);
     tok->decoding_readline = readline;
+    if (pos > 0) {
+        if (PyObject_CallObject(readline, NULL) == NULL) {
+            readline = NULL;
+            goto cleanup;
+        }
+    }
 
   cleanup:
     Py_XDECREF(stream);