In this paper, we introduce a simple Bessel |$\delta $| -method to the theory of exponential sums for |$\textrm{GL}_2$|. Some results of Jutila on exponential sums are generalized in a less technical manner to holomorphic newforms of arbitrary level and nebentypus. In particular, this gives a short proof for the Weyl-type subconvex bound in the |$t$| -aspect for the associated |$L$| -functions.