you just need to substitute the first line by nothing in $wanted. using .*? instead of .* in you first regexp also improves performances quite dramatically.

#!/usr/bin/perl -w

use strict;
use LWP::Simple;
my $data = get ("http://www.bloomberg.com/energy/index.html");
my ($wanted) = $data =~ /<!-+PETROLEUM-+>\s*(.*?)\s*<!-+POWER-+>/s;  #
+ the .*? speeds up processing considerably
$wanted=~ s/^[^\n]*\n//s;                # just remove the first line
open (FH,'>test_remline.txt') || die $!; # > creates a new file, >> ap
+pends
print FH $wanted;
close FH;    # not really necessary in this simple scrip
[download]

I feel I have to warn you that what you are doing is probably quite risky as you rely on comments in the HTML that Bloomberg can probably change at will, plus of course parsing HTML with regexps is not the best way to do it: you might want to look at HTML::Parser or HTML::TableExtract. And the .* construct leads to numerous problems described in Ovid's famous Death to Dot Star! post (although personally I don't have a problem with .*?).