The low kinetic energy and mass of the Crab supernova remnant challenge our understanding of core-collapse supernova explosions. A possibility is that the Crab nebula is surrounded by a shell of fast ejecta containing the ‘missing’ kinetic energy and mass. The only direct evidence for such a fast shell comes from an absorption feature in the Crab pulsar spectrum as a result of C ivλ1550. The velocities inferred from the C iv line absorption extend to at least ∼2500 km s−1, which is about twice as fast as the expansion of main shell of the remnant in our direction. We have searched for additional evidence of fast-moving ejecta in the optical spectra obtained with the FORS1 instrument at the European Southern Observatory (ESO) 8.2-m Very Large Telescope (VLT) and with the Andalucia Faint Object Spectrograph and Camera (ALFOSC) at the 2.56-m Nordic Optical Telescope (NOT), with the focus on absorption in Ca iiλλ3934,3968, and emission components in [O iii] λλ4959,5007. The data are compared with the C ivλ1550 absorption, and with theoretical expectations derived from shell models with ballistic gas motion, and a power-law density profile of the fast ejecta. Along the line of sight to the pulsar, we find that no gas in the nebula moves faster towards us than ≈1400 km s−1. We identify this gas as part of the known main shell of the remnant. This velocity agrees with previous results showing that the Crab nebula is moving slowly in this direction. It is slower than the velocity of 1680 km s−1 used in the models of Sollerman et al. as a minimum velocity of the presumed fast shell of supernova ejecta to account for the C iv line absorption. We find faster moving gas within 3–10 arcsec north and south of the pulsar, where the fastest gas moving towards us, as traced by [O iii], has a velocity of 1650–1700 km s−1. The fastest [O iii] emitting gas along the line of sight to the pulsar, on the rear side of the nebula, has a velocity of ≈+1800 km s−1, which is higher than the velocity previously recorded for that direction. However, neither the [O iii] nor Ca ii lines display any signatures of fast shell ejecta at the velocities inferred from the C iv line absorption. To fully rule out the possibility that a chimney-like structure directed towards us could be responsible for the C iv line absorption, we need deep observations taken with 8–10-m class telescopes with good spectral resolution. We show that a spectral resolution better than ∼200 km s−1 is needed to draw any conclusions on emission lines from gas moving towards us, along the line of sight of the pulsar, faster than ≈1700 km s−1. To probe the fast shell ejecta, new observations from the Hubble Space Telescope (HST) Cosmic Origins Spectrograph (COS) should be substantially more powerful than the previous HST Space Telescope Imaging Spectrograph (STIS) data to fully explore the C ivλ1550 absorption-line profile.