This paper presents a new interpretation of the non-solar isotopic composition of a series of elements from Si to Sm found in small-sized (μm) SiC grains of presumably circumstellar origin. It relies on a parametrized model that aims at investigating in as broad a way as possible the neutron exposures or range of such exposures that could replicate the series of measured isotopic compositions without relying on any specific (and sometimes highly uncertain) astrophysical scenario.It is 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 exposure than contemplated in previous studies. Such a neutron irradiation history does not necessitate the classical assumption of an admixture 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 different neutron exposures. In this framework, predictions are provided for all the elements from Si to Bi, and implications for possible astrophysical sites are discussed.