diff --git a/pep-0574.rst b/pep-0574.rst
index 1755f6a51..ed3f13ef7 100644
--- a/pep-0574.rst
+++ b/pep-0574.rst
@@ -227,16 +227,17 @@ Consumer API
    class Pickler:
       def __init__(self, file, protocol=None, ..., buffer_callback=None):
          """
-         If *buffer_callback* is not None, then it is called with a list
-         of out-of-band buffer views when deemed necessary (this could be
-         once every buffer, or only after a certain size is reached,
-         or once at the end, depending on implementation details). The
-         callback should arrange to store or transmit those buffers without
-         changing their order.
-
          If *buffer_callback* is None (the default), buffer views are
          serialized into *file* as part of the pickle stream.
 
+         If *buffer_callback* is not None, then it can be called any number
+         of times with a buffer view.  If the callback returns a false value
+         (such as None), the given buffer is out-of-band; otherwise the
+         buffer is serialized in-band, i.e. inside the pickle stream.
+
+         The callback should arrange to store or transmit out-of-band buffers
+         without changing their order.
+
          It is an error if *buffer_callback* is not None and *protocol* is
          None or smaller than 5.
          """
@@ -281,20 +282,29 @@ Three new opcodes are introduced:
   it on the stack.
 * ``READONLY_BUFFER`` makes a readonly view of the top of the stack.
 
-When pickling encounters a ``PickleBuffer``, there can be four cases:
+When pickling encounters a ``PickleBuffer``, that buffer can be considered
+in-band or out-of-band depending on the following conditions:
 
-* If a ``buffer_callback`` is given and the ``PickleBuffer`` is writable,
-  the ``PickleBuffer`` is given to the callback and a ``NEXT_BUFFER`` opcode
-  is appended to the pickle stream.
-* If a ``buffer_callback`` is given and the ``PickleBuffer`` is readonly,
-  the ``PickleBuffer`` is given to the callback and a ``NEXT_BUFFER`` opcode
-  is appended to the pickle stream, followed by a ``READONLY_BUFFER`` opcode.
-* If no ``buffer_callback`` is given and the ``PickleBuffer`` is writable,
-  it is serialized into the pickle stream as if it were a ``bytearray`` object.
-* If no ``buffer_callback`` is given and the ``PickleBuffer`` is readonly,
-  it is serialized into the pickle stream as if it were a ``bytes`` object.
+* if no ``buffer_callback`` is given, the buffer is in-band;
+* if a ``buffer_callback`` is given, it is called with the buffer.  If the
+  callback returns a true value, the buffer is in-band; if the callback
+  returns a false value, the buffer is out-of-band.
 
-The distinction between readonly and writable buffers is explained below
+An in-band buffer is serialized as follows:
+
+* If the buffer is writable, it is serialized into the pickle stream as if
+  it were a ``bytearray`` object.
+* If the buffer is readonly, it is serialized into the pickle stream as if
+  it were a ``bytes`` object.
+
+An out-of-band buffer is serialized as follows:
+
+* If the buffer is writable, a ``NEXT_BUFFER`` opcode is appended to the
+  pickle stream.
+* If the buffer is readonly, a ``NEXT_BUFFER`` opcode is appended to the
+  pickle stream, followed by a ``READONLY_BUFFER`` opcode.
+
+The distinction between readonly and writable buffers is motivated below
 (see "Mutability").