diff --git a/src/calibre/utils/smtp.py b/src/calibre/utils/smtp.py
index 7138b85c6e..3875fd1b83 100644
--- a/src/calibre/utils/smtp.py
+++ b/src/calibre/utils/smtp.py
@@ -18,7 +18,7 @@ def safe_localhost():
     # if that can't be calculated, that we should use a domain literal
     # instead (essentially an encoded IP address like [A.B.C.D]).
     fqdn = socket.getfqdn()
-    if '.' in fqdn:
+    if '.' in fqdn and fqdn != '.':
         # Some mail servers have problems with non-ascii local hostnames, see
         # https://bugs.launchpad.net/bugs/1256549
         try:
diff --git a/src/calibre/utils/smtplib.py b/src/calibre/utils/smtplib.py
index 83a0a7280c..820af3babf 100755
--- a/src/calibre/utils/smtplib.py
+++ b/src/calibre/utils/smtplib.py
@@ -279,7 +279,7 @@ class SMTP:
             # if that can't be calculated, that we should use a domain literal
             # instead (essentially an encoded IP address like [A.B.C.D]).
             fqdn = socket.getfqdn()
-            if '.' in fqdn:
+            if '.' in fqdn and fqdn != '.':
                 self.local_hostname = fqdn
             else:
                 # We can't find an fqdn hostname, so use a domain literal
@@ -800,6 +800,7 @@ class SMTP:
         self.close()
         return res
 
+
 if _have_ssl:
 
     class SMTP_SSL(SMTP):