sub that_cgi_script {
  ...
  eval { do_something() };
  ...
}
sub do_something {
  # 1) may return if everything ok
  # 2) may die on error, but such error non-important to
  #    calling code in above case and will be catched by
  #    eval and ignored
  # 3) may redirect: print Location header and call exit()
}

##</code><code>##

my $FCGI_EXIT = "FCGI NORMAL EXIT\n";
BEGIN { *CORE::GLOBAL::exit = sub { die $FCGI_EXIT }; }
while (CGI::Fast->new()) {
    eval { that_cgi_script(); };
    die $@ if $@ ne q{} && $@ ne $FCGI_EXIT;
    $CGI::Fast::Ext_Request->Finish();
}

##</code><code>##

BEGIN { *CORE::GLOBAL::exit = sub { goto EXIT }; }
while (CGI::Fast->new()) {
    eval { that_cgi_script(); };
    die $@ if $@ ne q{};
  EXIT:
    $CGI::Fast::Ext_Request->Finish();
}