This old example may help you. It shows how to use a timer to make a slight delay on the first bind, to wait and see if it's a combo. Your best bet, is just to make your bindings unique, so you don't have to worry about this. Do you really need <c><d>? Why not have <e> do what <c><d> is supposed to do?

#!/usr/bin/perl
use strict;
use Tk;

# by graff of perlmonks 
# The way that works is that the initial "button-1" event  
# will invoke "Tk::after" to schedule a call to "print_me"  
# after half a second, but a double-button-1 event will  
# call "print_me" immediately, with a parameter that makes  
# it behave in a special way. The logic associated with  
# that special parameter also has to "cancel" the Tk::after  
# object that had been scheduled by the button-1 event that  
# was the first half of the double-click. 

my $after_id;

my $mw = MainWindow->new();
$mw->Label(-text => "Type a phrase in the entry box below")->pack();
$mw->Label(-text => "Then click once to print all of it")->pack();
$mw->Label(-text => "Or double-click to print just one word")->pack();
my $ent = $mw->Entry(-width => 25)->pack();

$ent->bind( "<Double-Button-1>", [\&print_me, "word"] );
$ent->bind( "<Button-1>", sub {
         $after_id = $ent->after( 500, [\&print_me, $ent] )
           }
 );

MainLoop;

sub print_me
{
my ( $widget, $mode ) = @_;
my $content = $widget->get();
if ( $mode eq "word" ) {
$widget->afterCancel( $after_id );
my $start = $widget->index( 'sel.first' );
my $length = $widget->index( 'sel.last' ) - $start;
print "you double-clicked the word: " .
substr( $content, $start, $length), $/;
} else {
print $content,$/;
}
}
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