Starting up a process for each request unfortunately is too expensive

Then I would write one script that takes URLS from stdin and does the fetches.

#! perl -slw
use strict;
use LWP::Simple;

while( <> ) {
    chomp;
    my $content = get $_;
    ### do something with it.
}
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And then drive multiple copies of that script from a threaded script:

#! perl -slw
use strict;
use threads;
use Thread::Queue;

sub worker {
    my $Q = shift;

    open my $pipe, '-|', q[ perl theOtherScript.pl] or die $!;
    while( my $url = $Q->dequeue() ) {
        print $pipe $url;
    }    
}

our $THREADS //= 4;
my $Q = new Thread::Queue;

my @workers = map threads->create( \&worker, $Q ), 1 .. $THREADS;
$Q->enqueue( $url ) while ...; ## fetch urls from somewhere and Q them
$Q->enqueue( (undef) x $THREADS );
$_->join for @workers;
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Great suggestion, thank you. I've implemented this and it works beautifully.

I chose to use IPC::Open2 to get bi-di communication, sending single-line messages back and forth, so the script is now as functional as it would have been with a thread-safe Crypt::SSLeay.