The existence of the λ Boo type as a class of chemically-peculiar stars in its own right has taxed numerous researchers, and has challenged spectroscopists to produce a model which is plausible, comprehensive and predictive. Stars which are recognized as members of the λ Boo class have late-B to early-F spectral types, and exhibit (often substantially) low abundances of Fe-peak elements although elements such as C, N, O and S may have more nearly solar abundances. Since less than 2% of objects within the relevant spectral-type domain appear to be λ Boo stars their existence has demanded rather special conditions, and has triggered opinion that this group may not in fact exist but that each case can be explained as an unrecognized binary. In this paper we examine those claims by monitoring 10 stars, listed in the literature as possible λ Boo stars but said to be "likely candidates" for composite-spectrum binaries, by employing high-dispersion spectroscopy in an intermittent observing programme designed to reveal the sort of line-profile changes that should be detectable if each object were really a pair of similar stars in an SB2 system. We also monitor two other stars: HR 7903, said to be a binary (but is more like an Ap star), and λ Boo itself. The sample includes 1 possible, 1 marginal and 4 definite λ Boo classifications. In addition, we derive the physical properties of the 12 stars by photometric and spectroscopic synthesis, and measure their radial velocities. Three of the sample show small line-profile variations, but not of the sort that can be attributed to the presence of a companion star; they are the suspected Ap star HR 7903, HR 6878 (which exhibits spectrum peculiarities very similar to those of HR 7903 but has not previously been classified as Bp or Ap), and λ Aql, whose rapid spectrum variations resemble those observed in spotted or CP stars. None of the stars shows any evidence to suggest that it could be a composite-spectrum binary.