diff --git a/Doc/library/ssl.rst b/Doc/library/ssl.rst
--- a/Doc/library/ssl.rst
+++ b/Doc/library/ssl.rst
@@ -1588,8 +1588,17 @@
 Notes on non-blocking sockets
 -----------------------------
 
-When working with non-blocking sockets, there are several things you need
-to be aware of:
+SSL sockets behave slightly different than regular sockets in
+non-blocking mode. When working with non-blocking sockets, there are
+thus several things you need to be aware of:
+
+- Most :class:`SSLSocket` methods will raise either
+  :exc:`SSLWantWriteError` or :exc:`SSLWantReadError` instead of
+  :exc:`BlockingIOError` if an I/O operation would
+  block. However, **the** :meth:`SSLSocket.send` **method returns zero in
+  this situation** instead of raising any exception (this behavior is
+  mostly a historical accident that has not bene changed for
+  backwards compatibility reasons).
 
 - Calling :func:`~select.select` tells you that the OS-level socket can be
   read from (or written to), but it does not imply that there is sufficient
@@ -1615,7 +1624,8 @@
         except ssl.SSLWantWriteError:
             select.select([], [sock], [])
 
-
+  
+  
 .. _ssl-security:
 
 Security considerations
diff --git a/Modules/_io/textio.c b/Modules/_io/textio.c
--- a/Modules/_io/textio.c
+++ b/Modules/_io/textio.c
@@ -1470,6 +1470,15 @@
             Py_DECREF(state);
             return -1;
         }
+
+        if (!PyBytes_Check(dec_buffer)) {
+            PyErr_Format(PyExc_TypeError,
+                         "decoder getstate() should have returned a bytes "
+                         "object, not '%.200s'",
+                         Py_TYPE(dec_buffer)->tp_name);
+            Py_DECREF(state);
+            return -1;
+        }
         Py_INCREF(dec_buffer);
         Py_INCREF(dec_flags);
         Py_DECREF(state);
@@ -1482,21 +1491,22 @@
     chunk_size = PyLong_FromSsize_t(Py_MAX(self->chunk_size, size_hint));
     if (chunk_size == NULL)
         goto fail;
+
     input_chunk = PyObject_CallMethodObjArgs(self->buffer,
         (self->has_read1 ? _PyIO_str_read1: _PyIO_str_read),
         chunk_size, NULL);
     Py_DECREF(chunk_size);
     if (input_chunk == NULL)
         goto fail;
-    if (!PyBytes_Check(input_chunk)) {
+    if (!PyObject_CheckBuffer(input_chunk)) {
         PyErr_Format(PyExc_TypeError,
-                     "underlying %s() should have returned a bytes object, "
+                     "underlying %s() should have returned a bytes-like object, "
                      "not '%.200s'", (self->has_read1 ? "read1": "read"),
                      Py_TYPE(input_chunk)->tp_name);
         goto fail;
     }
 
-    nbytes = PyBytes_Size(input_chunk);
+    nbytes = PySequence_Size(input_chunk);
     eof = (nbytes == 0);
 
     if (Py_TYPE(self->decoder) == &PyIncrementalNewlineDecoder_Type) {
@@ -1523,18 +1533,12 @@
         /* At the snapshot point, len(dec_buffer) bytes before the read, the
          * next input to be decoded is dec_buffer + input_chunk.
          */
-        PyObject *next_input = PyNumber_Add(dec_buffer, input_chunk);
-        if (next_input == NULL)
-            goto fail;
-        if (!PyBytes_Check(next_input)) {
-            PyErr_Format(PyExc_TypeError,
-                         "decoder getstate() should have returned a bytes "
-                         "object, not '%.200s'",
-                         Py_TYPE(next_input)->tp_name);
-            Py_DECREF(next_input);
+        PyObject *next_input = dec_buffer;
+        PyBytes_Concat(&next_input, input_chunk);
+        if (next_input == NULL) {
+            dec_buffer = NULL; // Reference lost to PyBytes_Concat
             goto fail;
         }
-        Py_DECREF(dec_buffer);
         Py_CLEAR(self->snapshot);
         self->snapshot = Py_BuildValue("NN", dec_flags, next_input);
     }