diff --git a/management/univention-directory-manager-modules/modules/univention/admin/handlers/__init__.py b/management/univention-directory-manager-modules/modules/univention/admin/handlers/__init__.py
index 0b5a34a95a..5a340f5b14 100644
--- a/management/univention-directory-manager-modules/modules/univention/admin/handlers/__init__.py
+++ b/management/univention-directory-manager-modules/modules/univention/admin/handlers/__init__.py
@@ -2050,7 +2050,7 @@ def __modify_dhcp_object(self, position, mac, ip=None):
 				univention.debug.debug(univention.debug.ADMIN, univention.debug.INFO, 'the host "%s" already has a dhcp object, so we search for the next free uv name' % (name))
 				RE = re.compile(r'cn=[^,]+_uv(\d+),')
 				taken = set(int(m.group(1)) for m in (RE.match(dn) for dn in results) if m)
-				n = min(set(range(max(taken) + 1)) - taken) if taken else 0
+				n = min(set(range(max(taken) + 2)) - taken) if taken else 0
 				name = '%s_uv%d' % (name, n)
 
 			dn = 'cn=%s,%s' % (escape_dn_chars(name), position)