We bound a short second moment average of $\mathrm{GL}(3)$ and $\mathrm{GL}(3) \times \mathrm{GL}(1)$ $L$-functions. These yield $t$-aspect and depth aspect subconvexity bounds respectively, and improve upon the earlier subconvexity exponents. This moment estimate provides an analogue for cusp forms of Ivic’s bound for the sixth moment of the zeta function, and is the first time a short second moment has been used to obtain a subconvex bound in higher rank. This is a joint work with Ritabrata Munshi and Wing Hong Leung.