diff --git a/IPython/core/payload.py b/IPython/core/payload.py
index 429e005..c95fcdb 100644
--- a/IPython/core/payload.py
+++ b/IPython/core/payload.py
@@ -29,11 +29,17 @@ class PayloadManager(Configurable):
 
     _payload = List([])
 
-    def write_payload(self, data, update=False):
+    def write_payload(self, data, single=True):
+        """Include or update the specified `data` payload in the PayloadManager.
+
+        If a previous payload with the same source than `data` exists
+        and `single` is True, it will be overwritten with the new one.
+        """
+
         if not isinstance(data, dict):
             raise TypeError('Each payload write must be a dict, got: %r' % data)
 
-        if update and 'source' in data:
+        if single and 'source' in data:
             source = data['source']
             for i, pl in enumerate(self._payload):
                 if 'source' in pl and pl['source'] == source:
diff --git a/IPython/kernel/zmq/zmqshell.py b/IPython/kernel/zmq/zmqshell.py
index 62d2cb8..df7f5a5 100644
--- a/IPython/kernel/zmq/zmqshell.py
+++ b/IPython/kernel/zmq/zmqshell.py
@@ -583,7 +583,7 @@ class ZMQInteractiveShell(InteractiveShell):
             source='set_next_input',
             text=text
         )
-        self.payload_manager.write_payload(payload, update=True)
+        self.payload_manager.write_payload(payload)
     
     #-------------------------------------------------------------------------
     # Things related to magics