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Recently the author established an improvement of the classical Vietoris sineinequality to include sine polynomials with non-monotone coefficients.  In this paper two further improvements are presented admitting sinepolynomials with non-monotone and non-decaying coefficients.  The extremal sums of the two results have the coefficient sequences {2a, a,4/3, 1, 6/5, 1, 8/7, 1, ...}, where a = 0.78265..., and {3, 3/2, 7/3, 7/4,11/5, 11/6, ...}.

Improved Vietoris Sine Inequalities for Non-Monotone, Non-Decaying Coefficients