Hi Perl Monks!

I've finished writing a script, and now I want for it to print all messages both to screen and to a (log) file. So a little googling pointed me to this File::Tee module. Installed it (locally as I'm not root) and ran just a basic example.
But I have a problem making it work with STDIN. Here is a little code that doesn't work right, or at least it doesn't work as I thought it should.

#!/usr/bin/perl -w
use lib '/path/to/local/lib/';
use File::Tee qw(tee);

################
## No bug yet ##
################

#Print Starting Info
print ("=============================\n");
print ("  Just a simple bug example \n");
print ("=============================\n\n");

# Get user input
print ("Enter anything:   ");
$CODE = <>;
chomp ($CODE);
print ("You used $CODE!\n=============================\n\n");


################
## Here it is ##
################

# Start with Tee
tee(STDOUT, '>', 'logfile.txt');

#Print Starting Info
print ("=============================\n");
print ("  Just a simple bug example \n");
print ("=============================\n\n");

# Get user input
print ("Enter anything:   ");
$CODE2 = <>;
chomp ($CODE2);
print ("You used $CODE2!\n=============================\n\n");
[download]

It works right until it comes to the tee(...) part. Then it just waits for my blind input before printing the input message... Here is the output

=============================
  Just a simple bug example
=============================

Enter anything:   PerlMonks
You used PerlMonks!
=============================

=============================
  Just a simple bug example
=============================

TeeTestPM
perl/teetest> Enter anything:   You used TeeTestPM!
=============================
[download]

Anyone could help out?

Thanks a bunch!
Cheers!