Tuti Interweaving is a systematic approach for weaving halftoned (monochrome) images in Jacquard looms, presented by Ahmed and Deussen in Bridges 2017. It uses alternating black and white yarns for both warp and weft, and applies a preset weaving structure for half of the fabric, leaving the rest to render the desired image. In this paper we discuss alternatives that use white weft and black warp, or vise versa. We also address a situation where Tuti Interweaving would not guarantee a sturdy fabric as supposed.