A possible solution to the difficult problem of geometrical distortion of watermarked images in a blind watermarking scenario is to use a template grid in the autocorrelation function. However, the important drawback of this method is that the watermark itself can be estimated and subtracted, or the peaks in the Fourier magnitude spectrum can be removed. A recently proposed solution is to modulate the watermark with a pattern derived from the image content and a secret key. This effectively hides the watermark pattern, making malicious attacks much more difficult. However, the algorithm to compute the modulation pattern is computationally intensive. We propose an efficient implementation, using frequency domain filtering, to make this hiding method more practical. Furthermore, we evaluate the performance of different kinds of modulation patterns. We present experimental results showing the influence of template hiding on detection and payload extraction performance. The results also show that modulating the ACF based watermark improves detection performance when the modulation signal can be retrieved sufficiently accurately. Modulation signals with small average periods between zero crossings provide the most watermark detection improvement. Using these signals, the detector can also make the most errors in retrieving the modulation signal until the detection performance drops below the performance of the watermarking method without modulation.