diff --git a/man3/iconv.3 b/man3/iconv.3
index 0dfcd7d14..7a8d78504 100644
--- a/man3/iconv.3
+++ b/man3/iconv.3
@@ -140,7 +140,6 @@ An incomplete multibyte sequence has been encountered in the input.
 .SH VERSIONS
 This function is available in glibc since version 2.1.
 .SH ATTRIBUTES
-.SS Multithreading (see pthreads(7))
 For an explanation of the terms used in this section, see
 .BR attributes (7).
 .TS
@@ -150,8 +149,15 @@ l l l.
 Interface	Attribute	Value
 T{
 .BR iconv ()
-T}	Thread safety	MT-Safe
+T}	Thread safety	MT-Safe race:cd
 .TE
+.PP
+The
+.BR iconv ()
+function is MT-Safe, as long as callers arrange for
+mutual exclusion on the
+.I cd
+argument.
 .SH CONFORMING TO
 POSIX.1-2001.
 .SH NOTES
diff --git a/man3/iconv_open.3 b/man3/iconv_open.3
index 40ceeec8f..61845ae6e 100644
--- a/man3/iconv_open.3
+++ b/man3/iconv_open.3
@@ -76,8 +76,6 @@ the state is in the initial state.
 Using
 .BR iconv (3)
 modifies the descriptor's conversion state.
-(This implies that a conversion
-descriptor can not be used in multiple threads simultaneously.)
 To bring the state back to the initial state, use
 .BR iconv (3)
 with NULL as