diff --git a/MySQLdb/MySQLdb/cursors.py b/MySQLdb/MySQLdb/cursors.py
index f39124a..bf69f90 100644
--- a/MySQLdb/MySQLdb/cursors.py
+++ b/MySQLdb/MySQLdb/cursors.py
@@ -29,7 +29,7 @@ class BaseCursor(object):
         self.connection = connection
         self.description = None
         self.rowcount = -1
-        self.arraysize = 100
+        self.arraysize = 1
         self._executed = None
         self.lastrowid = None
         self.messages = []
diff --git a/MySQLdb/_mysql.c b/MySQLdb/_mysql.c
index 68ff2f8..647f7e6 100644
--- a/MySQLdb/_mysql.c
+++ b/MySQLdb/_mysql.c
@@ -609,6 +609,10 @@ _mysql_ConnectionObject_close(
 		mysql_close(&(self->connection));
 		Py_END_ALLOW_THREADS
 		self->open = 0;
+	} else {
+		PyErr_SetString(_mysql_ProgrammingError,
+				"closing a closed connection");
+		return NULL;
 	}
 	_mysql_ConnectionObject_clear(self);
 	Py_INCREF(Py_None);