SLF4JBridgeHandler.removeHandlersForRootLogger();
//Handler handler = new ConsoleHandler();
Handler handler = new SLF4JBridgeHandler(); 
handler.setFilter(new Filter() { 
	@Override
	public boolean isLoggable(LogRecord record) {
		return record.getMessage().startsWith("ShouldBeShown");
	}
});
Logger julLogger = Logger.getLogger("com.myLogger");
julLogger.addHandler(handler);
julLogger.setLevel(Level.FINEST);
julLogger.info("ShouldNotBeShown info message");
julLogger.info("ShouldBeShown info message");

09:39:01.604 [main] INFO  com.myLogger - ShouldNotBeShown info message
09:39:01.607 [main] INFO  com.myLogger - ShouldBeShown info message

Nov 25, 2015 9:39:37 AM de.harrassowitz.test.dho.jul.JulFilterTest main
INFO: ShouldBeShown info message

Handler handler = new SLF4JBridgeHandler() {
    @Override
    public void publish(LogRecord record) {
        if (getFilter() != null && !getFilter().isLoggable(record)) {
            return;
        }
        super.publish(record);
    }
};