Keep script running after sending response, is possible?

In order to achieve faster end user response times for certain operations, is it possible to keep the php script running (for exemple for continue accessing database) after sending the response to the client? I have tried to use register_shutdown_function() but it doesn't works as desired. I have also tried flush(), but it doesn't work very well either... I mean the very same script in the same hosting enviroment don't works the first time you use it, but only afterwards... plus the client browser keeps waiting for more data until the script actually ends. Not very cool. Is there some way to solve this problem? Thank you Oriol de San Pedro