diff --git a/Lib/test/test_binascii.py b/Lib/test/test_binascii.py
index a631a6abbe0..cd76dbbc637 100755
--- a/Lib/test/test_binascii.py
+++ b/Lib/test/test_binascii.py
@@ -108,6 +108,9 @@ class BinASCIITest(unittest.TestCase):
 
         self.assertRaises(binascii.Error, binascii.b2a_uu, 46*b"!")
 
+        # Issue #7701 (crash on a pydebug build)
+        self.assertEqual(binascii.b2a_uu(b'x'), b'!>   \n')
+
     def test_crc32(self):
         crc = binascii.crc32(b"Test the CRC-32 of")
         crc = binascii.crc32(b" this string.", crc)
diff --git a/Misc/NEWS b/Misc/NEWS
index f2e2fed6ca6..b2203064d6e 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -213,6 +213,9 @@ C-API
 Library
 -------
 
+- Issue #7701: Fix crash in binascii.b2a_uu() in debug mode when given a
+  1-byte argument.  Patch by Victor Stinner.
+
 - Issue #3299: Fix possible crash in the _sre module when given bad
   argument values in debug mode.  Patch by Victor Stinner.
 
diff --git a/Modules/binascii.c b/Modules/binascii.c
index 51101b412a5..833283f7c98 100644
--- a/Modules/binascii.c
+++ b/Modules/binascii.c
@@ -294,7 +294,7 @@ binascii_b2a_uu(PyObject *self, PyObject *args)
 	}
 
 	/* We're lazy and allocate to much (fixed up later) */
-	if ( (rv=PyBytes_FromStringAndSize(NULL, bin_len*2+2)) == NULL ) {
+	if ( (rv=PyBytes_FromStringAndSize(NULL, 2 + (bin_len+2)/3*4)) == NULL ) {
 		PyBuffer_Release(&pbin);
 		return NULL;
 	}