This paper presents a new interpretation of the non-solar isotopic com
position of a series of elements from Si to Sm found in small-sized (m
um) SiC grains of presumably circumstellar origin. It relies on a para
metrized model that aims at investigating in as broad a way as possibl
e the neutron exposures or range of such exposures that could replicat
e the series of measured isotopic compositions without relying on any
specific (and sometimes highly uncertain) astrophysical scenario. It i
s found that the general trends of the isotopic data of Si, Ca, Ti, Sr
, Kr, Xe, Ba, Nd and Sm can be reproduced with a much weaker neutron e
xposure than contemplated in previous studies. Such a neutron irradiat
ion history does not necessitate the classical assumption of an admixt
ure of a s-process component to normal solar abundances. Instead, the
linear correlations observed in three-isotope plots are interpreted in
terms of a mixture of components having experienced slightly differen
t neutron exposures. In this framework, predictions are provided for a
ll the elements from Si to Bi, and implications for possible astrophys
ical sites are discussed.