  We revisit the evaluation of one-loop modular integrals in string theory,
employing new methods that, unlike the traditional 'orbit method', keep
T-duality manifest throughout. In particular, we apply the
Rankin-Selberg-Zagier approach to cases where the integrand function grows at
most polynomially in the IR. Furthermore, we introduce new techniques in the
case where `unphysical tachyons' contribute to the one-loop couplings. These
methods can be viewed as a modular invariant version of dimensional
regularisation. As an example, we treat one-loop BPS-saturated couplings
involving the $d$-dimensional Narain lattice and the invariant Klein
$j$-function, and relate them to (shifted) constrained Epstein Zeta series of
O(d,d;Z). In particular, we recover the well-known results for d=2 in a few
easy steps.
