  A population of X-ray dominated gamma-ray bursts (GRBs) observed by Ginga,
BeppoSax and Hete-2 should be represented in the BATSE data as presumably soft
bursts. We have performed a search for soft GRBs in the BATSE records in the
25--100 keV energy band. A softness of a burst spectrum can be a reason why it
has been missed by the on-board procedure and previous searches for untriggered
GRBs tuned to 50--300 keV range. We have found a surprisingly small number
(~20/yr down to 0.1 ph cm$^{-2}$ s$^{-1}$) of soft GRBs where the count rate is
dominated by 25--50 keV energy channel. This fact as well as the analysis of
HETE-2 and common BeppoSAX/BATSE GRBs indicates that the majority of GRBs with
a low Epeak has a relatively hard tail with the high-energy power-law photon
index >-3. An exponential cutoff in GRB spectra below 20 keV may be a
distinguishing feature separating non-GRB events.
