package My::Class;
use vars qw( $VERSION );
BEGIN { $VERSION= 1.001 }

package My::Class::_internal;

sub My::Class::new {
    my $self= bless {}, "My::Class::_object";
    #...
    return $self;
}

sub utilityFunction {
    my $self= shift @_;
    # ...
}

sub My::Class::_object::method {
    my $self= shift @_;
    # ...
    utilityFunction( $self, @args );
    # ...
}

##</code><code>##

    # Calling a class method via an object:
    my $obj2= $obj1->new();

    # Calling an object method via the class name:
    my $ret= My::Class->method()

    # Using my utility function:
    $obj->utilityFunction();

##</code><code>##

    *My::Class::_object::new= \&My::Class::new;

##</code><code>##

package My::Class;
use vars qw( $VERSION );
BEGIN { $VERSION= 1.001 }

# Following line moved down to increase robustness:
## My::Class::_internal->import( ":DEFAULT" );

package My::Class::_internal;

require Exporter;
use vars qw( @EXPORT_OK );
BEGIN {
    *import= \&Exporter::import;
    @EXPORT_OK= qw( new method );
}

sub utilityFunction {
    my $self= shift @_;
    # ...
}

sub new {
    my $class= shift @_;
    my $proto;
    $class= ref( $proto= $class )   if  ref $class;
    my $self= bless {}, $class;
    #...
    return $self;
}

sub method {
    my $self= shift @_;
    # ...
    utilityFunction( $self, @args );
    # ...
}

package My::Class;
My::Class::_internal->import( ":DEFAULT" );

##</code><code>##

    package My::Class;
    use My::Class::_internal;