  Generalizing and unifying prior results, we solve the subconvexity problem
for the $L$-functions of $\GL_{1}$ and $\GL_{2}$ automorphic representations
over a fixed number field, uniformly in all aspects. A novel feature of the
present method is the softness of our arguments; this is largely due to a
consistent use of canonically normalized period relations, such as those
supplied by the work of Waldspurger and Ichino--Ikeda.
