The original LDSS deep redshift survey showed that the bulk of the faint blue galaxies brighter than bJ = 22.5 are at redshifts less than z = 0.5. However, the 19 per cent incompleteness of the survey left open the possibility that some small subset of the galaxy population may be at high redshift (z > 0.7) and have subsequently undergone strong luminosity evolution. With new observations we have now reduced the incompleteness in two of the original survey zones to just 4.5 per cent. No galaxies with z > 0.7 were found, confirming the previous results. The 90 per cent confidence upper limit on the number of high-redshift galaxies brighter than bJ = 22.5 is consistent with no evolution but inconsistent with any significant luminosity evolution of L > L* galaxies. The 99 per cent limit is consistent with no more than 1.0–1.2 magnitudes of luminosity evolution by a redshift of z = 1. We have also carried out a deeper survey of the bluest galaxies with 22 < R < 23. Redshifts were obtained for 11 out of 23 objects with B – R ≤ 0.70 and/or R – I ≤ 0.75. Most importantly, the redshifts of all six galaxies with B – I < 1, indicative of a near-flat spectrum in fv, were identified. Apart from one QSO, the identified objects all have z < 1. The observation that all the flat-spectrum objects are at low redshift rules out galaxy evolution models with mild luminosity evolution only (low q0 , high zf), which predict that almost all galaxies with these colours should have z > 1. The luminosities of the galaxies with near-flat spectra span the range of 0.15 L* to 0.02 L*, from normal galaxies to dwarfs. These results are consistent both with merging-dominated models for galaxy evolution and with models postulating bursts of star formation in dwarf galaxies. Infrared-selected redshift surveys and multicolour high-resolution imaging offer means to discriminate between these scenarios.