  Let $g$ be a fixed Hecke cusp form for $\mathrm{SL}(2,\mathbb{Z})$ and $\chi$
be a primitive Dirichlet character of conductor $M$. The best known subconvex
bound for $L(1/2,g\otimes \chi)$ is of Burgess strength. The bound was proved
by a couple of methods: shifted convolution sums and the Petersson/Kuznetsov
formula analysis. It is natural to ask what inputs are really needed to prove a
Burgess-type bound on $\rm GL(2)$. In this paper, we give a new proof of the
Burgess-type bounds ${L(1/2,g\otimes \chi)\ll_{g,\varepsilon}
M^{1/2-1/8+\varepsilon}}$ and $L(1/2,\chi)\ll_{\varepsilon}
M^{1/4-1/16+\varepsilon}$ that does not require the basic tools of the previous
proofs and instead uses a trivial delta method.
