diff --git a/doc/ssl/SSL_read.pod b/doc/ssl/SSL_read.pod
index 6b47f2fbd..f6c37f77e 100644
--- a/doc/ssl/SSL_read.pod
+++ b/doc/ssl/SSL_read.pod
@@ -83,11 +83,13 @@ bytes actually read from the TLS/SSL connection.
 
 =item 0
 
-The read operation was not successful, the SSL connection was closed by the
-peer by sending a "close notify" alert. The SSL_RECEIVED_SHUTDOWN flag in
-the ssl shutdown state is set (see L<SSL_shutdown(3)|SSL_shutdown(3)>,
-L<SSL_set_shutdown(3)|SSL_set_shutdown(3)>).
-Call SSL_get_error() with the return value B<ret> to find out,
+The read operation was not successful. The reason may either be a clean
+shutdown due to a "close notify" alert sent by the peer (in which case
+the SSL_RECEIVED_SHUTDOWN flag in the ssl shutdown state is set
+(see L<SSL_shutdown(3)|SSL_shutdown(3)>,
+L<SSL_set_shutdown(3)|SSL_set_shutdown(3)>). It is also possible, that
+the peer simply shut down the underlying transport and the shutdown is
+incomplete. Call SSL_get_error() with the return value B<ret> to find out,
 whether an error occurred or the connection was shut down cleanly
 (SSL_ERROR_ZERO_RETURN).
 
diff --git a/doc/ssl/SSL_write.pod b/doc/ssl/SSL_write.pod
index 7299f6e2e..dfa42e9ae 100644
--- a/doc/ssl/SSL_write.pod
+++ b/doc/ssl/SSL_write.pod
@@ -78,12 +78,8 @@ bytes actually written to the TLS/SSL connection.
 
 =item 0
 
-The write operation was not successful, because the write side of the
-SSL connection was shut down (the SSL_SENT_SHUTDOWN flag in the shutdown
-state is set) by calling L<SSL_shutdown(3)|SSL_shutdown(3)> or
-L<SSL_set_shutdown(3)|SSL_set_shutdown(3)>. It is also possible, that the
-underlying connection was closed.
-Call SSL_get_error() with the return value B<ret> to find out,
+The write operation was not successful. Probably the underlying connection
+was closed. Call SSL_get_error() with the return value B<ret> to find out,
 whether an error occurred or the connection was shut down cleanly
 (SSL_ERROR_ZERO_RETURN).