A plastic container of the type that may be formed from a material such as PET using the stretch blow molding process includes a main body portion and a base portion that is characterized by a relatively tall and narrow profile above the standing ring and that has a deep inset recess defined therein. The deep inset recess is defined in part by an upstanding inner sidewall portion adjacent to the standing ring that has a height that may be greater than about 0.35 inch. The upstanding inner sidewall portion may have a substantially straight portion that is substantially parallel to a substantially straight portion of an outer sidewall of the base.