diff --git a/src/OpenSSL/crypto.py b/src/OpenSSL/crypto.py
index 2362f6d..56dad18 100644
--- a/src/OpenSSL/crypto.py
+++ b/src/OpenSSL/crypto.py
@@ -1314,11 +1314,13 @@
         """
         Return the issuer of this certificate.
 
-        This creates a new :py:class:`X509Name`: modifying it does not affect
-        this certificate.
+        This creates a new :class:`X509Name` that wraps the underlying issuer
+        name field on the certificate. Modifying it will modify the underlying
+        certificate, and will have the effect of modifying any other
+        :class:`X509Name` that refers to this issuer.
 
         :return: The issuer of this certificate.
-        :rtype: :py:class:`X509Name`
+        :rtype: :class:`X509Name`
         """
         return self._get_name(_lib.X509_get_issuer_name)
 
@@ -1337,11 +1339,13 @@
         """
         Return the subject of this certificate.
 
-        This creates a new :py:class:`X509Name`: modifying it does not affect
-        this certificate.
+        This creates a new :class:`X509Name` that wraps the underlying subject
+        name field on the certificate. Modifying it will modify the underlying
+        certificate, and will have the effect of modifying any other
+        :class:`X509Name` that refers to this subject.
 
         :return: The subject of this certificate.
-        :rtype: :py:class:`X509Name`
+        :rtype: :class:`X509Name`
         """
         return self._get_name(_lib.X509_get_subject_name)