diff --git a/Doc/c-api/init.rst b/Doc/c-api/init.rst
index 1a54321..6439d7f 100644
--- a/Doc/c-api/init.rst
+++ b/Doc/c-api/init.rst
@@ -93,12 +93,12 @@
       single: main()
       triple: stdin; stdout; sdterr
 
-   This function should be called before :c:func:`Py_Initialize`. It
-   specifies which encoding and error handling to use with standard io,
-   with the same meanings as in :func:`str.encode`.
+   This function should be called before :c:func:`Py_Initialize`, if it is
+   called at all. It specifies which encoding and error handling to use
+   with standard IO, with the same meanings as in :func:`str.encode`.
 
    It overrides :envvar:`PYTHONIOENCODING` values, and allows embedding code
-   to control io encoding when the environment variable does not work.
+   to control IO encoding when the environment variable does not work.
 
    ``encoding`` and/or ``errors`` may be NULL to use
    :envvar:`PYTHONIOENCODING` and/or default values (depending on other
@@ -110,7 +110,10 @@
    If :c:func:`Py_Finalize` is called, this function will need to be called
    again in order to affect subsequent calls to :c:func:`Py_Initialize`.
 
-   Returns 0 if successful.
+   Returns 0 if successful, a nonzero value on error (e.g. calling after the
+   interpreter has already been initialized).
+
+   .. versionadded:: 3.4
 
 
 .. c:function:: void Py_SetProgramName(wchar_t *name)
diff --git a/Include/pythonrun.h b/Include/pythonrun.h
index 4cc4dcd..7f67ab7 100644
--- a/Include/pythonrun.h
+++ b/Include/pythonrun.h
@@ -28,8 +28,13 @@
 PyAPI_FUNC(void) Py_SetPythonHome(wchar_t *);
 PyAPI_FUNC(wchar_t *) Py_GetPythonHome(void);
 
+#ifndef Py_LIMITED_API
+/* Only used by applications that embed the interpreter and need to
+ * override the standard encoding determination mechanism
+ */
 PyAPI_FUNC(int) Py_SetStandardStreamEncoding(const char *encoding,
                                              const char *errors);
+#endif
 
 PyAPI_FUNC(void) Py_Initialize(void);
 PyAPI_FUNC(void) Py_InitializeEx(int);
diff --git a/Python/pythonrun.c b/Python/pythonrun.c
index 3bcc474..b963ce1 100644
--- a/Python/pythonrun.c
+++ b/Python/pythonrun.c
@@ -148,11 +148,17 @@
         /* This is too late to have any effect */
         return -1;
     }
+    /* Can't call PyErr_NoMemory() on errors, as Python hasn't been
+     * initialised yet.
+     *
+     * However, the raw memory allocators are initialised appropriately
+     * as C static variables, so _PyMem_RawStrdup is OK even though
+     * Py_Initialize hasn't been called yet.
+     */
     if (encoding) {
         _Py_StandardStreamEncoding = _PyMem_RawStrdup(encoding);
         if (!_Py_StandardStreamEncoding) {
-            PyErr_NoMemory();
-            return -1;
+            return -2;
         }
     }
     if (errors) {
@@ -161,8 +167,7 @@
             if (_Py_StandardStreamEncoding) {
                 PyMem_RawFree(_Py_StandardStreamEncoding);
             }
-            PyErr_NoMemory();
-            return -1;
+            return -3;
         }
     }
     return 0;