In this paper, we show that there is a family of polynomials \{P_n\}, where P_n is a polynomial in n variables of degree at most d = O(\log^2 n), such that

1. P_n can be computed by linear sized homogeneous depth-5 circuits.

2. P_n can be computed by poly(n) sized non-homogeneous depth-3 circuits.

3. Any homogeneous depth-4 circuit computing P_n must have size at least n^{\Omega(\sqrt{d})}.

This shows that the parameters for the depth reduction results of Agrawal and Vinay[av08, koiran, Tav13] are tight for extremely restricted classes of arithmetic circuits, for instance homogeneous depth-5 circuits and non-homogeneous depth-3 circuits, and over an appropriate range of parameters, qualitatively improve a result of Kumar and Saraf [KS14], which showed that the parameters of depth reductions are optimal for algebraic branching programs.