Well, the variable being bound incorrectly is the second ($start_item) not the first ($self->param('catalog_id')). However, the ideas hold true. I did try:

$sth -> execute(
     $self -> param('catalog_id'),
     0 + $start_item,
     20
 );
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without success. Also $start_item + 0 and int($start_item). I just tried the specific type binding you recommended, and that did work:

$sth->bind_param(1, $self->param('catalog_id'), SQL_INTEGER);
$sth->bind_param(2, $start_item, SQL_INTEGER);
$sth->bind_param(3, 20, SQL_INTEGER);
$sth->execute();
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This leads me to believe I am experiencing a bug in DBI. (My database is MySQL.) However, this still begs the question, how is DBI evaluating the result of int($start_item) differently than the $this_stupid_counter above?