It sounds like you have a limited number of conditions (the different levels of verbosity), so you could something like the following:

use constant MAX_VERBOSITY => 5;

sub vprint {
   # Or whatever.
   our $msg; local *msg = \($_[0]);
   print("$msg\n");
}

BEGIN {
   my $verbosity = $ARGV[0] || 0;  # Or whatever
   my $eval = '';
   for (1..MAX_VERBOSITY) {
      $eval .= ($_ <= $verbosity
         ? "*vprint$_ = \&vprint;\n"
         : "use constant vprint$_ => 1;\n"
      );
   }
   eval $eval."1;\n" or die $@;
}

vprint1("msg1");  # Optimized away if arg is < 1
vprint2("msg2");  # Optimized away if arg is < 2
vprint3("msg3");  # Optimized away if arg is < 3
vprint4("msg4");  # Optimized away if arg is < 4
vprint5("msg5");  # Optimized away if arg is < 5
[download]

Update: Ah woops! There'll be a prototype mismatch. The best you can do (without playing with the opcode tree) is:

use constant MAX_VERBOSITY => 5;

BEGIN {
   my $verbosity = $ARGV[0] || 0;  # Or whatever
   my $eval = '';
   for (1..MAX_VERBOSITY) {
      my $allow = ($_ <= $verbosity) ? 1 : 0;
      $eval .= "use constant V$_ => $allow;\n";
   }
   eval $eval."1;\n" or die $@;
}

sub vprint {
   # Or whatever.
   our $msg; local *msg = \($_[0]);
   print("$msg\n");
}

vprint("msg1") if V1;  # Optimized away if arg is < 1
vprint("msg2") if V2;  # Optimized away if arg is < 2
vprint("msg3") if V3;  # Optimized away if arg is < 3
vprint("msg4") if V4;  # Optimized away if arg is < 4
vprint("msg5") if V5;  # Optimized away if arg is < 5
[download]

Tested

>perl -MO=Terse 645574.pl 3
LISTOP (0x1986d80) leave [1]
    OP (0x1986864) enter
    COP (0x1986da4) nextstate
    UNOP (0x1986e00) entersub [2]
        UNOP (0x1986e3c) null [141]
            OP (0x1986e20) pushmark
            SVOP (0x1986e60) const [7] PV (0x182ff6c) "msg1"
            UNOP (0x1986e80) null [17]
                PADOP (0x1986ea0) gv  GV (0x191a7f4) *vprint
    COP (0x1986c64) nextstate
    UNOP (0x1986cc0) entersub [4]
        UNOP (0x1986cfc) null [141]
            OP (0x1986ce0) pushmark
            SVOP (0x1986d20) const [8] PV (0x191a7d0) "msg2"
            UNOP (0x1986d40) null [17]
                PADOP (0x1986d60) gv  GV (0x191a7f4) *vprint
    COP (0x1986b24) nextstate
    UNOP (0x1986b80) entersub [6]
        UNOP (0x1986bbc) null [141]
            OP (0x1986ba0) pushmark
            SVOP (0x1986be0) const [9] PV (0x191a7b8) "msg3"
            UNOP (0x1986c00) null [17]
                PADOP (0x1986c20) gv  GV (0x191a7f4) *vprint
    COP (0x19869e4) nextstate
    OP (0x1986a20) null [5]
    COP (0x19868a4) nextstate
    OP (0x19868e0) null [5]
645574.pl syntax OK

>perl -MO=Terse 645574.pl 3
msg1
msg2
msg3
[download]

I'm betting this is the fastest you'll get.