Configure Eclipse logging for Exceptions and Errors

Configure Eclipse logging for Exceptions and Errors

Is there a good way, either by configuring the built-in console or using a
plugin, to configure and filter the logging output for Exceptions and
Errors and their stacktraces in Eclipse?
Example problem this would help with:
I use a web framework where Exceptions in the business logic always result
in a StackOverflowError ultimately being thrown by the framework when a
page is rendered, because the page rendering relied on that logic running
successfully.
This means when a problem occurs in the business logic, the Exception
stacktrace I want to look at can only be found by scrolling up above a
massive StackOverflowError stacktrace, which always occurs last and
contains no useful information.
I'd like to have the option to do one or more of the following
Do not log anything for StackOverflowErrors
Log only the fact a StackOverflowError has been thrown, with no stacktrace
limit the logging of StackOverflowError stacktrace to the top few lines
The dialog I get to from Right Click > Preferences in the console on
Eclipse Kepler does not offer any of the above.