package BDB::PPALogin;

use strict;
BEGIN {
     require Exporter;
     our @ISA = qw (Exporter);
     our @EXPORT = qw ( isSuper has_priv [...] );
}

##</code><code>##

package BDB::pinfo;
[ other code / use statements ]

sub canSeeMe {
     eval {
          if ( isSuper() ) {
               # This used to work, but now fails
          }
     }
     eval {
          if ( BDB::PPALogin::isSuper() ) {
               # This has always worked, but I *really* don't want to type the package name in code every time...
          }
     }
}