The second-order half-linear neutral delay difference equation obtains some improved oscillatory solutions in this research. Δ ???? ???? Δ???? ???? ???? +???? ???? ???????? ????−???? =0, ????≥????0, where????>0is an odd positive integer quotient. Our findings in this work are crisp and improved on some of the literature's well-known oscillatory results. Some examples are provided to highlight our primary findings.2020 Mathematics Subject Classifications: 39A12, 39A21.