diff --git a/ChangeLog b/ChangeLog
index 02586e0b..fb151882 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,9 @@
+2002-09-06  Akim Demaille  <akim@epita.fr>
+
+	* doc/autoconf.texi (Setting Output Variables): Clarify what
+	precious variables are.
+	Suggested by Pontus Skoeld.
+
 2002-09-05  Akim Demaille  <akim@epita.fr>
 
 	* bin/Makefile.am (autoconf, autoheader, autoreconf, autoupdate)
diff --git a/THANKS b/THANKS
index 16915771..19682b23 100644
--- a/THANKS
+++ b/THANKS
@@ -144,6 +144,7 @@ Peter Eisentraut            peter_e@gmx.net
 Peter Simons                simons@research.cys.de
 Peter Stephenson            pws@csr.com
 Philipp Thomas              kthomas@gwdg.de
+Pontus Skoeld               pont@soua.net
 Rainer Orth                 ro@TechFak.Uni-Bielefeld.DE
 Raja R Harinath             harinath@cs.umn.edu
 Ralf Corsepius              corsepiu@faw.uni-ulm.de
diff --git a/doc/autoconf.texi b/doc/autoconf.texi
index 04af77ec..165769b3 100644
--- a/doc/autoconf.texi
+++ b/doc/autoconf.texi
@@ -6219,11 +6219,18 @@ Being precious means that
 @var{variable} is @code{AC_SUBST}'d.
 
 @item
-@var{variable} is kept in the cache including if it was not specified on
-the @samp{./configure} command line.  Indeed, while @command{configure}
-can notice the definition of @code{CC} in @samp{./configure
-CC=bizarre-cc}, it is impossible to notice it in @samp{CC=bizarre-cc
-./configure}, which, unfortunately, is what most users do.
+The value of @var{variable} when @command{configure} was launched is
+saved in the cache, including if it was not specified on the command
+line but via the environment.  Indeed, while @command{configure} can
+notice the definition of @code{CC} in @samp{./configure CC=bizarre-cc},
+it is impossible to notice it in @samp{CC=bizarre-cc ./configure},
+which, unfortunately, is what most users do.
+
+We emphasize that it is the @emph{initial} value of @var{variable} which
+is saved, not that found during the execution of @command{configure}.
+Indeed, specifying @samp{./configure FOO=foo} and letting
+@samp{./configure} guess that @code{FOO} is @code{foo} can be two very
+different runs.
 
 @item
 @var{variable} is checked for consistency between two