diff --git a/Doc/lib/libzlib.tex b/Doc/lib/libzlib.tex
index b9726d7..b0bc881 100644
--- a/Doc/lib/libzlib.tex
+++ b/Doc/lib/libzlib.tex
@@ -123,24 +123,29 @@
 Decompression objects support the following methods, and two attributes:
 
 \begin{memberdesc}{unused_data}
-A string which contains any unused data from the last string fed to
-this decompression object.  If the whole string turned out to contain
-compressed data, this is \code{""}, the empty string. 
+A string which contains any bytes past the end of the compressed data.
+That is, this remains \code{""} until the last byte that contains
+compression data is available.  If the whole string turned out to
+contain compressed data, this is \code{""}, the empty string.
 
 The only way to determine where a string of compressed data ends is by
 actually decompressing it.  This means that when compressed data is
 contained part of a larger file, you can only find the end of it by
-reading data and feeding it into a decompression object's
-\method{decompress} method until the \member{unused_data} attribute is
-no longer the empty string.  
+reading data and feeding it followed by some non-empty string into a
+decompression object's \method{decompress} method until the
+\member{unused_data} attribute is no longer the empty string.
 \end{memberdesc}
 
 \begin{memberdesc}{unconsumed_tail}
 A string that contains any data that was not consumed by the last
 \method{decompress} call because it exceeded the limit for the
-uncompressed data buffer.
+uncompressed data buffer.  This data has not yet been seen by the zlib
+machinery, so you must feed it (possibly with further data
+concatenated to it) back to a subsequent \method{decompress} method
+call in order to get correct output.
 \end{memberdesc}
 
+
 \begin{methoddesc}[Decompress]{decompress}{string}{\optional{max_length}}
 Decompress \var{string}, returning a string containing the
 uncompressed data corresponding to at least part of the data in