diff --git a/doc/man3/X509_cmp.pod b/doc/man3/X509_cmp.pod
index a4e18dfb585bb5b9277b8a82dd4cc81d0a7902af..7460d901db0d59c0f9116964e12ad58dddc35621 100644
--- a/doc/man3/X509_cmp.pod
+++ b/doc/man3/X509_cmp.pod
@@ -25,16 +25,20 @@ This set of functions are used to compare X509 objects, including X509
 certificates, X509 CRL objects and various values in an X509 certificate.
 
 The X509_cmp() function compares two B<X509> objects indicated by parameters
-B<a> and B<b>. The comparison is based on the B<memcmp> result of the hash
+I<a> and I<b>. The comparison is based on the B<memcmp> result of the hash
 values of two B<X509> objects and the canonical (DER) encoding values.
 
 The X509_NAME_cmp() function compares two B<X509_NAME> objects indicated by
-parameters B<a> and B<b>. The comparison is based on the B<memcmp> result of
-the canonical (DER) encoding values of the two objects. L<i2d_X509_NAME(3)>
-has a more detailed description of the DER encoding of the B<X509_NAME> structure.
+parameters I<a> and I<b>. The comparison is based on the B<memcmp> result of the
+canonical (DER) encoding values of the two objects using L<i2d_X509_NAME(3)>.
+This procedure adheres to the matching rules for Distinguished Names (DN)
+given in RFC 4517 section 4.2.15 and RFC 5280 section 7.1.
+In particular, the order of Relative Distinguished Names (RDNs) is relevant.
+On the other hand, if an RDN is multi-valued, i.e., it contains a set of
+AttributeValueAssertions (AVAs), its members are effectively not ordered.
 
 The X509_issuer_and_serial_cmp() function compares the serial number and issuer
-values in the given B<X509> objects B<a> and B<b>.
+values in the given B<X509> objects I<a> and I<b>.
 
 The X509_issuer_name_cmp(), X509_subject_name_cmp() and X509_CRL_cmp() functions
 are effectively wrappers of the X509_NAME_cmp() function. These functions compare
@@ -47,8 +51,8 @@ of just the issuer name.
 
 =head1 RETURN VALUES
 
-The B<X509> comparison functions return B<-1>, B<0>, or B<1> if object B<a> is
-found to be less than, to match, or be greater than object B<b>, respectively.
+The B<X509> comparison functions return B<-1>, B<0>, or B<1> if object I<a> is
+found to be less than, to match, or be greater than object I<b>, respectively.
 
 X509_NAME_cmp(), X509_issuer_and_serial_cmp(), X509_issuer_name_cmp(),
 X509_subject_name_cmp() and X509_CRL_cmp() may return B<-2> to indicate an error.