The presence of submicron grains has been inferred in several debris discs, despite the fact that these particles should be blown out by stellar radiation pressure on very short timescales. So far, no fully satisfying explanation has been found for this apparent paradox. We investigate the possibility that the observed abundances of submicron grains could be naturally produced in bright debris discs, where the high collisional activity produces them at a rate high enough to partially compensate for their rapid removal. We also investigate to what extent this potential presence of small grains can affect our understanding of some debris disc characteristics. We use a code following the collisional evolution of a debris disc down to submicron grains far below the limiting blow-out size $s_{blow}$. We explore different configurations: A and G stars, cold and warm discs, bright and very bright systems. We find that, in bright discs (fractional luminosity $>10^{-3}$) around A stars, there is always a high-enough amount of submicron grains to leave detectable signatures, both in scattered-light, where the discs color becomes blue, and in the mid-IR ($10<lambda<20mu$m), where it boosts the discs luminosity by at least a factor of 2 and induces a pronounced silicate solid-state band around $10mu$m. We also show that, with this additional contribution of submicron grains, the SED can mimic that of two debris belts separated by a factor of 2 in radial distance. For G stars, the effect of $s<s_{blow}$ grains remains limited in the spectra, in spite of the fact that they dominate the systems geometrical cross section. We also find that, for all considered cases, the halo of small (bound and unbound) grains that extends far beyond the main disc contributes to $sim50$% of the flux up to $lambdasim50mu$m wavelengths.
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