We present our current results of an off-line search for non-triggered gamma-ray bursts (GRBs) in the BATSE daily records (obtained with 1024 ms time resolution) covering about 8.6 years of observations. We found 1713 non-triggered and 1963 triggered GRBs. The scan was done with artificial test bursts added to the data which allowed us to measure the efficiency of the search. We extended thelog&hthinsp;N−log&hthinsp;Pdistribution down toP∼0.1&hthinsp;ph/s/cm2.Previous indications of a turnover of thelog&hthinsp;N−log&hthinsp;Pdistribution at smallPare not confirmed. ©2000 American Institute of Physics.