Warning when using AXIS under Weblogic

[MB...@unicacorp.com]

Apologies in advance for a newbie question, and double apologies
if I'm posting this in the wrong place:

I've got a simple test program to try different session management
techniques.  However, each time a client starts a session,
Weblogic 8.1 generates the following error message (line breaks
added):

<Jan 7, 2004 11:37:20 AM EST> <Warning> <HTTP Session> <BEA-100061> 
<Web application: ServletContext(id=2144034,name=axis,context-path=/axis)
tried to place a non-serializable attribute: TestSession into the session: 

181AqMYbRfzRiOK5Ee2w4EaP3QjGVcrzLTnpyA9o2v9aQKeHGVij!367587242!1073493440957.
This attribute will be lost upon redeployment. This message is logged only
once per session.>

To paraphrase "Becket," Can no one rid me of this meddlesome warning?
Thanks in advance!

Mike B.

Details:
The class "TestSession" is defined thusly:
public class TestSession implements java.io.Serializable
{
        public TestSession()
        {
        }

        public String echo(String arg) throws RemoteException
        {
                MessageContext     mc      = 
MessageContext.getCurrentContext();
                Session            session = mc.getSession();
                Integer            count2  = new Integer(0);
 
                if  (session == null)
                        throw new RemoteException("No session in 
MessageContext!");
                count2 = (Integer)session.get("counter");
            if  (count2 == null)
                count2 = new Integer(0);
            count2 = new Integer(count2.intValue() + 1);
            session.set("counter", count2);

                return arg + " " + count2;
        }
}

The wsdd file reads as follows (again, with line breaks added):
<deployment xmlns="http://xml.apache.org/axis/wsdd/"
     xmlns:java="http://xml.apache.org/axis/wsdd/providers/java">
 <handler type="java:org.apache.axis.handlers.SimpleSessionHandler" 
name="session"/>
 <service name="TestSession" provider="java:RPC">
  <parameter name="className" value="soap.test.TestSession"/>
  <parameter name="allowedMethods" value="*"/>
  <parameter name="scope" value="Session"/>
 </service>
</deployment>