diff --git a/Doc/library/binascii.rst b/Doc/library/binascii.rst
--- a/Doc/library/binascii.rst
+++ b/Doc/library/binascii.rst
@@ -20,8 +20,13 @@ higher-level modules.
 
 .. note::
 
-   Encoding and decoding functions do not accept Unicode strings.  Only bytestring
-   and bytearray objects can be processed.
+   ``a2b_*`` functions accept Unicode strings containing only ASCII characters.
+   Other functions only accept bytes and bytes-compatible objects (such as
+   bytearray objects and other objects implementing the buffer API).
+
+   .. versionchanged:: 3.3
+      ASCII-only unicode strings are now accepted by the ``a2b_*`` functions.
+
 
 The :mod:`binascii` module defines the following functions:
 
diff --git a/Lib/test/test_binascii.py b/Lib/test/test_binascii.py
--- a/Lib/test/test_binascii.py
+++ b/Lib/test/test_binascii.py
@@ -208,9 +208,9 @@ class BinASCIITest(unittest.TestCase):
             except Exception as err:
                 self.fail("{}({!r}) raises {!r}".format(func, empty, err))
 
-    def test_unicode_strings(self):
-        # Unicode strings are not accepted.
-        for func in all_functions:
+    def test_unicode_b2a(self):
+        # Unicode strings are not accepted by b2a_* functions.
+        for func in set(all_functions) - set(a2b_functions) | {'rledecode_hqx'}:
             try:
                 self.assertRaises(TypeError, getattr(binascii, func), "test")
             except Exception as err:
@@ -218,6 +218,34 @@ class BinASCIITest(unittest.TestCase):
         # crc_hqx needs 2 arguments
         self.assertRaises(TypeError, binascii.crc_hqx, "test", 0)
 
+    def test_unicode_a2b(self):
+        # Unicode strings are accepted by b2a_* functions.
+        MAX_ALL = 45
+        raw = self.rawdata[:MAX_ALL]
+        for fa, fb in zip(a2b_functions, b2a_functions):
+            if fa == 'rledecode_hqx':
+                # Takes non-ASCII data
+                continue
+            a2b = getattr(binascii, fa)
+            b2a = getattr(binascii, fb)
+            try:
+                a = b2a(self.type2test(raw))
+                binary_res = a2b(a)
+                a = a.decode('ascii')
+                res = a2b(a)
+            except Exception as err:
+                self.fail("{}/{} conversion raises {!r}".format(fb, fa, err))
+            if fb == 'b2a_hqx':
+                # b2a_hqx returns a tuple
+                res, _ = res
+                binary_res, _ = binary_res
+            self.assertEqual(res, raw, "{}/{} conversion: "
+                             "{!r} != {!r}".format(fb, fa, res, raw))
+            self.assertEqual(res, binary_res)
+            self.assertIsInstance(res, bytes)
+            # non-ASCII string
+            self.assertRaises(ValueError, a2b, "\x80")
+
 
 class ArrayBinASCIITest(BinASCIITest):
     def type2test(self, s):
diff --git a/Modules/binascii.c b/Modules/binascii.c
--- a/Modules/binascii.c
+++ b/Modules/binascii.c
@@ -183,6 +183,44 @@ static unsigned short crctab_hqx[256] = 
     0x6e17, 0x7e36, 0x4e55, 0x5e74, 0x2e93, 0x3eb2, 0x0ed1, 0x1ef0,
 };
 
+static int
+ascii_buffer_converter(PyObject *arg, Py_buffer *buf)
+{
+    if (arg == NULL) {
+        PyBuffer_Release(buf);
+        return 1;
+    }
+    if (PyUnicode_Check(arg)) {
+        if (PyUnicode_READY(arg) < 0)
+            return 0;
+        if (!PyUnicode_IS_ASCII(arg)) {
+            PyErr_SetString(PyExc_ValueError,
+                            "string argument should contain only ASCII characters");
+            return 0;
+        }
+        assert(PyUnicode_KIND(arg) == PyUnicode_1BYTE_KIND);
+        buf->buf = (void *) PyUnicode_1BYTE_DATA(arg);
+        buf->len = PyUnicode_GET_LENGTH(arg);
+        buf->obj = NULL;
+        return 1;
+    }
+    if (PyObject_GetBuffer(arg, buf, PyBUF_SIMPLE) != 0) {
+        PyErr_Format(PyExc_TypeError,
+                     "argument should be bytes, buffer or ASCII string, "
+                     "not %R", Py_TYPE(arg));
+        return 0;
+    }
+    if (!PyBuffer_IsContiguous(buf, 'C')) {
+        PyErr_Format(PyExc_TypeError,
+                     "argument should be a contiguous buffer, "
+                     "not %R", Py_TYPE(arg));
+        PyBuffer_Release(buf);
+        return 0;
+    }
+    return Py_CLEANUP_SUPPORTED;
+}
+
+
 PyDoc_STRVAR(doc_a2b_uu, "(ascii) -> bin. Decode a line of uuencoded data");
 
 static PyObject *
@@ -196,7 +234,7 @@ binascii_a2b_uu(PyObject *self, PyObject
     PyObject *rv;
     Py_ssize_t ascii_len, bin_len;
 
-    if ( !PyArg_ParseTuple(args, "y*:a2b_uu", &pascii) )
+    if ( !PyArg_ParseTuple(args, "O&:a2b_uu", ascii_buffer_converter, &pascii) )
         return NULL;
     ascii_data = pascii.buf;
     ascii_len = pascii.len;
@@ -370,7 +408,7 @@ binascii_a2b_base64(PyObject *self, PyOb
     Py_ssize_t ascii_len, bin_len;
     int quad_pos = 0;
 
-    if ( !PyArg_ParseTuple(args, "y*:a2b_base64", &pascii) )
+    if ( !PyArg_ParseTuple(args, "O&:a2b_base64", ascii_buffer_converter, &pascii) )
         return NULL;
     ascii_data = pascii.buf;
     ascii_len = pascii.len;
@@ -546,7 +584,7 @@ binascii_a2b_hqx(PyObject *self, PyObjec
     Py_ssize_t len;
     int done = 0;
 
-    if ( !PyArg_ParseTuple(args, "y*:a2b_hqx", &pascii) )
+    if ( !PyArg_ParseTuple(args, "O&:a2b_hqx", ascii_buffer_converter, &pascii) )
         return NULL;
     ascii_data = pascii.buf;
     len = pascii.len;
@@ -1119,7 +1157,7 @@ binascii_unhexlify(PyObject *self, PyObj
     char* retbuf;
     Py_ssize_t i, j;
 
-    if (!PyArg_ParseTuple(args, "y*:a2b_hex", &parg))
+    if (!PyArg_ParseTuple(args, "O&:a2b_hex", ascii_buffer_converter, &parg))
         return NULL;
     argbuf = parg.buf;
     arglen = parg.len;
@@ -1197,8 +1235,8 @@ binascii_a2b_qp(PyObject *self, PyObject
     static char *kwlist[] = {"data", "header", NULL};
     int header = 0;
 
-    if (!PyArg_ParseTupleAndKeywords(args, kwargs, "y*|i", kwlist, &pdata,
-          &header))
+    if (!PyArg_ParseTupleAndKeywords(args, kwargs, "O&|i:a2b_qp", kwlist,
+                                     ascii_buffer_converter, &pdata, &header))
         return NULL;
     data = pdata.buf;
     datalen = pdata.len;