Using improved Doppler tomographic signal-analysis techniques, we have carried out a deep search for starlight reflected from the giant planet orbiting the star τ Bootis. We combined echelle spectra secured at the 4.2-m William Herschel telescope in 1998 and 1999 (which yielded a tentative detection of a reflected starlight component from the orbiting companion) with new data obtained in 2000 (which failed to confirm the detection). The combined data set comprises 893 high-resolution spectra with a total integration time of 75h 32m spanning 17 nights. We establish an upper limit on the planet's geometric albedo p < 0.39 (at the 99.9 per cent significance level) at the most probable orbital inclination i≃ 36°, assuming a grey albedo, a Venus-like phase function and a planetary radius Rp= 1.2RJup. We are able to rule out some combinations of the predicted planetary radius and atmospheric albedo models with high, reflective cloud decks. Although a weak candidate signal appears near to the most probable radial velocity amplitude, its statistical significance is insufficient for us to claim a detection with any confidence.