diff --git a/doc/sources/tutorial-hpack.rst b/doc/sources/tutorial-hpack.rst
index 3ad22a6e..36e82d9d 100644
--- a/doc/sources/tutorial-hpack.rst
+++ b/doc/sources/tutorial-hpack.rst
@@ -78,15 +78,16 @@ header data.  To initialize the object, use
 
     int nghttp2_hd_inflate_new(nghttp2_hd_inflater **inflater_ptr);
 
-To inflate header data, use `nghttp2_hd_inflate_hd()`::
+To inflate header data, use `nghttp2_hd_inflate_hd2()`::
 
-    ssize_t nghttp2_hd_inflate_hd(nghttp2_hd_inflater *inflater,
-                                  nghttp2_nv *nv_out, int *inflate_flags,
-                                  uint8_t *in, size_t inlen, int in_final);
+    ssize_t nghttp2_hd_inflate_hd2(nghttp2_hd_inflater *inflater,
+                                   nghttp2_nv *nv_out, int *inflate_flags,
+                                   const uint8_t *in, size_t inlen,
+                                   int in_final);
 
-`nghttp2_hd_inflate_hd()` reads a stream of bytes and outputs a single
-header field at a time. Multiple calls are normally required to read a
-full stream of bytes and output all of the header fields.
+`nghttp2_hd_inflate_hd2()` reads a stream of bytes and outputs a
+single header field at a time. Multiple calls are normally required to
+read a full stream of bytes and output all of the header fields.
 
 The *inflater* is the inflater object initialized above.  The *nv_out*
 is a pointer to a :type:`nghttp2_nv` into which one header field may
@@ -118,7 +119,7 @@ If *in_final* is zero and the :macro:`NGHTTP2_HD_INFLATE_EMIT` flag is
 not set, it indicates that all given data was processed.  The caller
 is required to pass additional data.
 
-Example usage of `nghttp2_hd_inflate_hd()` is shown in the
+Example usage of `nghttp2_hd_inflate_hd2()` is shown in the
 `inflate_header_block()` function in `deflate.c`_.
 
 Finally, to delete a :type:`nghttp2_hd_inflater` object, use
diff --git a/lib/includes/nghttp2/nghttp2.h b/lib/includes/nghttp2/nghttp2.h
index 0ed36051..78435578 100644
--- a/lib/includes/nghttp2/nghttp2.h
+++ b/lib/includes/nghttp2/nghttp2.h
@@ -4768,10 +4768,14 @@ NGHTTP2_EXTERN ssize_t nghttp2_hd_inflate_hd(nghttp2_hd_inflater *inflater,
  *
  * The application should call this function repeatedly until the
  * ``(*inflate_flags) & NGHTTP2_HD_INFLATE_FINAL`` is nonzero and
- * return value is non-negative.  This means the all input values are
- * processed successfully.  Then the application must call
- * `nghttp2_hd_inflate_end_headers()` to prepare for the next header
- * block input.
+ * return value is non-negative.  If that happens, all given input
+ * data (|inlen| bytes) are processed successfully.  Then the
+ * application must call `nghttp2_hd_inflate_end_headers()` to prepare
+ * for the next header block input.
+ *
+ * In other words, if |in_final| is nonzero, and this function returns
+ * |inlen|, you can assert that :enum:`NGHTTP2_HD_INFLATE_FINAL` is
+ * set in |*inflate_flags|.
  *
  * The caller can feed complete compressed header block.  It also can
  * feed it in several chunks.  The caller must set |in_final| to