This article aims at lightweight, blind detection of additive spread-spectrum watermarks in the DWT domain. We focus on two host signal noise models and two types of hypothesis tests for watermark detection. As a crucial point of our work we take a closer look at the computational requirements of watermark detectors. This involves the computation of the detection response, parameter estimation and threshold selection. We show that by switching to approximate host signal parameter estimates or even fixed parameter settings we achieve a remarkable improvement in runtime performance without sacrificing detection performance. Our experimental results on a large number of images confirm the assumption that there is not necessarily a tradeoff between computation time and detection performance.