PL/SQL Buffer overflow

I am using DBMS_OUTPUT.PUT_LINE to debug some messages from my PL/SQL block. Of late, I have been getting the ORA-20000: ORU-10027: buffer overflow, limit of 1000000 bytes errors when users try to execute this package. I read that every time the package finishes execution, the data from buffer is written to the screen and then flushed. I have confirmed that with a single execution, this proc does not write that many bytes to the output. What else could be the cause ? Can I manually free up the buffer contents ?

Thanks,
Shiva.

you are filling it up - no you cant flush