Recently, Brα and Brγ emission was detected in the infrared spectrum of the B0.2V star τ Scorpii, without noticeable emission in Hα (Waters et al. A&A 272, L9-L12, 1993). Here we present simple HI recombination line calculations in the infrared and in the optical that demonstrate that there could be a class of B stars with low-density discs, a factor of 100 lower in density compared to normal Be stars, which may have escaped detection so far.