Summary: We show that every circuit with \(\mathrm{AND}\), \(\mathrm{OR}\), \(\mathrm{NOT}\), and \(\mathrm{MOD}_m\) gates, \(m\in\mathbb{Z}^+\), of polynomial size and depth \(d\) can be reduced to a depth-2, \(\mathrm{SYM}\circ\mathrm{AND}\), circuit of size \(2^{(\log n)^{O(d)}}\). This is an exponential size improvement over the traditional Yao-Beigel-Tarui, which has size blowup \(2^{(\log n)^{2^{O(d)}}}\). Therefore, depth-reduction for composite \(m\) matches the size of the Allender-Hertrampf construction for primes from 1989. We also list two among the consequences of our construction. One immediate implication is a near-exponential improvement in the depth, from \(o(\log\log n)\) to \(o(\log n/\log\log n)\), in Williams' program for \(\mathrm{NEXP}\) circuit lower bounds. In fact, this pushes William's program to the \(\mathrm{NC}^1\) frontier. Another, but nontrivial, implication is the strengthening of this \(o(\log n/\log\log n)\) depth lower bound in the Chattopadhyay-Santhanam interactive compression setting.