Linear circuit complexity classes
It follows from work of Valiant [1, 2] that linear-size $\textrm{NC}^1$ can be simulated by $2^{O(n / \log \log n)}$-size circuits of depth three and unbounded fan-in.

For a nice exposition of this result, see section 3 of the survey by Viola [3].

[1] Leslie G. Valiant. Graph-theoretic arguments in low-level complexity. In: Mathematical Foundations of Computer Science 1977. MFCS 1977. Lecture Notes in Computer Science, vol 53. Springer, Berlin, Heidelberg.

[2] Leslie G. Valiant. Exponential lower bounds for restricted monotone circuits. In: Proceedings of the fifteenth annual ACM symposium on Theory of computing (STOC '83). ACM, New York, NY, USA, 110-117.

[3] Emanuele Viola. On the power of small-depth computation
. Foundations and Trends in Theoretical Computer Science, vol. 5, num. 1, pp. 1--72, 2009.