Selection of starbursts through either deep narrow-band imaging of redshifted Lyα emitters, or localisation of host galaxies of gamma-ray bursts both give access to starburst galaxies that are significantly fainter than what is currently available from selection techniques based on the continuum (such as Lyman-break selection). Here we present results from a survey for Lyα emitters at z=3, conducted with the European Southern Observatory's Very Large Telescope. Furthermore, we briefly describe the properties of host galaxies of gamma-ray bursts atz > 2. The majority of both Lyα and gamma-ray burst-selected starbursts are fainter than the flux limit of the Lyman-break galaxy sample, suggesting that a significant fraction of the integrated star formation at z ≈ 3 is located in galaxies at the faint end of the luminosity function.