diff --git a/chapter08/pkgmgt.xml b/chapter08/pkgmgt.xml
index 3640b519d..daa1040b5 100644
--- a/chapter08/pkgmgt.xml
+++ b/chapter08/pkgmgt.xml
@@ -391,7 +391,16 @@ make DESTDIR=/usr/pkg/libfoo/1.1 install</userinput></screen>
     overriding the architecture-specific optimization to produce libraries
     suitable for both the host system and the system(s) where you'll deploy
     the LFS system.  Otherwise you'll get <computeroutput>Illegal
-    Instruction</computeroutput> errors running LFS.</para></important>
+    Instruction</computeroutput> errors running LFS.</para>
+
+    <para>The GMP build system stores the architecture-specific optimization
+    option used to build GMP into <filename>gmp.h</filename>, and the build
+    system of some package using GMP can read it from the header and use it
+    when building the package itself.  At least the MPFR build system is
+    known to do so.  Thus simply rebuilding GMP on a complete LFS system
+    is not enough: you'll need to recompile MPFR and maybe other packages
+    using GMP if you want to <quote>convert</quote> a complete LFS system
+    to be used for a different CPU.</para></important>
 
     <para>Finally, the new system has to be made bootable via <xref
     linkend="ch-bootable-grub"/>.</para>