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We prove that there exist at least cd⁵ monic irreducible nonreciprocal polynomials with integer coefficients of degree at most d whose Mahler measures are smaller than 2, where c is some absolute positive constant. These polynomials are constructed as nonreciprocal divisors of some Newman hexanomials $1+x^{r₁}+\cdots +x^{r₅}$, where the integers 1 ≤ r₁ < ⋯ < r₅ ≤ d satisfy some restrictions including $2r_j<r_{j+1}$ for j = 1,2,3,4. This result improves the previous lower bound cd³ and seems to be closer to the correct value of...