In data from three clear nights of echelle spectroscopy in 2000 October/November, and using improved Doppler tomographic signal-analysis techniques, we have carried out a deep search for starlight reflected from the innermost of v (upsilon) And's three planets. We place upper limits on the planet's radius R-P as functions of its projected orbital velocity K-P approximate to 139 sin i km s (1) for various assumptions about the wavelength-dependent geometric albedo spectrum p(lambda) of its atmosphere. For a grey albedo p we find Rprootp < 0.98 R-j, with 0.1 per cent false-alarm probability (4 sigma). For a Sudarsky, Burrows & Pinto Class V model atmosphere, the mean albedo in our 380-676 nm bandpass is [p] similar to 0.42, requiring R-P < 1.51 R-J, whereas an (isolated) Class IV model with [p] similar to 0.19 requires R-P < 2.23 R-J. The star's v(rot) sin i similar to 10 km s(-1) and estimated rotation period P-rot similar to 10 d suggest a high orbital inclination i similar to 70 degrees-80 degrees. We also develop methods for assessing the false-alarm probabilities of faint candidate detections, and for extracting information about the albedo spectrum and other planetary parameters from faint reflected-light signals.