def METHOD_NAME(self, x, y, z, pilImageAllowed=False, numpyAllowed=False, **kwargs):
    self._xyzInRange(x, y, z)
    tilename = '%d_%d.%s' % (x, y, self._info['Format'])
    tilepath = os.path.join(self._tiledir, '%d' % (self._baselevel + z), tilename)
    if self._nested:
        tilepath = os.path.join(tilepath, tilename)
    tile = PIL.Image.open(tilepath)
    overlap = int(self._info.get('Overlap', 0))
    tile = tile.crop((
        overlap if x else 0, overlap if y else 0,
        self.tileWidth + (overlap if x else 0),
        self.tileHeight + (overlap if y else 0)))
    return self._outputTile(tile, TILE_FORMAT_PIL, x, y, z,
                            pilImageAllowed, numpyAllowed, **kwargs)