great.

I had looked at the $| option and had declared it equal to 1 at the beginning of the script, but it didn't do anything (perhaps because I was using select to change the default output before printing?).

What finally worked was adding the $| = 1 between the selects. So, I went from this:

                                # Change the output to logfile
                                $filehandle = select LOG_FILENAME;

                                eval $menu[$var];

                                # Restore the filehandle
                                select $filehandle;
[download]

to this:

                                # Change the output to logfile
                                $filehandle = select LOG_FILENAME;

                                $| = 1;
                                eval $menu[$var];

                                # Restore the filehandle
                                select $filehandle;
[download]

Many thanks to all.