  We applied the Bayesian blocks representation technique to search for the
dimmest bursts from two magnetars: we identified 320 events from SGR J0501+4516
using a deep XMM-Newton observation and 404 bursts from SGR J1550-5418 using
two Swift/XRT pointings. The fluence level of our sample for both sources are
about 1-2 orders of magnitude lower than earlier studies. We systematically
investigated morphological characteristics and duration distributions of these
bursts, as these properties are directly obtained from their Bayesian blocks
profiles. We also studied the spectral behavior of the dimmest bursts, which
were grouped based on the morphological types and fluences. Our results helped
us further differentiate the spectral nature of very dim bursts from that of
the persistent emission, both fitted with physically motivated continuum
emission models. Moreover, we generated the differential burst fluence
distribution for these two magnetars in the lowest fluence regime.
